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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption 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href="//www.newsama.com/journals/afs/" aria-label="Advances in Fuzzy Systems">模糊系统的研究进展</一种>/<一种CL.一种S.S.=“S.C-HT.P.Nat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/afs/contents/year/2009/" aria-label="2009">2009年</一种>/<S.。P.一种N.CL.一种S.S.=“S.C-B.HL.BdH UVThf">文章</S.。P.一种N.> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</B.。你T.T.O.N.> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在本页</P.> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link 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class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <p class="sc-kZmsYB bkiEfx article_type">研究文章|<GyD.F4.y2B.一种!-- -->开放获取</P.> <div class="sc-RcBXQ ztvYg article_citation"> 体积<GyD.F4.y2B.一种!-- --> 2009年<GyD.F4.y2B.一种!-- --> <span class="sc-fZwumE cUsFHx">|</S.。P.一种N.>文章ID.<GyD.F4.y2B.一种!-- --> 303042.<GyD.F4.y2B.一种!-- --> <span class="sc-fZwumE cUsFHx">|</S.。P.一种N.> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2009/303042" aria-label="Doi-link">https://doi.org/10.1155/2009/303042</一种> </div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>艾哈迈德，Athar Kharal<GyD.F4.y2B.一种!-- -->那<GyD.F4.y2B.一种!-- --> “<S.。P.一种N.CL.一种S.S.=“一种D.just-article-svg-size">模糊套，模糊S开和S封闭映射</S.。P.一种N.>“，<GyD.F4.y2B.一种!-- --><i>模糊系统的研究进展</一世>那<GyD.F4.y2B.一种!-- --> 卷。<GyD.F4.y2B.一种!-- -->2009年<GyD.F4.y2B.一种!-- -->那<GyD.F4.y2B.一种!-- --> 文章ID.<GyD.F4.y2B.一种!-- -->303042.<GyD.F4.y2B.一种!-- -->那<GyD.F4.y2B.一种!-- --> 5.<GyD.F4.y2B.一种!-- -->   页面<GyD.F4.y2B.一种!-- -->那<GyD.F4.y2B.一种!-- --> 2009年<GyD.F4.y2B.一种!-- -->．<GyD.F4.y2B.一种!-- --> https://doi.org/10.1155/2009/303042</P.> </div> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引文</B.。你T.T.O.N.> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN gbcGIy article_title adjust-article-svg-size heading-title">模糊套，模糊S开和S封闭映射</H1> </div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class="">B. Ahmad.<S.。你P.>1<GyD.F4.y2B.一种!-- -->那<GyD.F4.y2B.一种!-- -->2</S.。你P.>和</S.。P.一种N.> <span class=""><b>Athar Kharal.</B.。GyD.F4.y2B.一种><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><a class="sc-htpNat bUhGXt link" href="http://orcid.org/0000-0002-7540-3424" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-iybRtq iQSObO" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a><sup>1</S.。你P.></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</S.。你P.><span>巴哈丁扎卡里亚大学纯粹和应用数学高级研究中心，巴基斯坦木尔坦60800</S.。P.一种N.></p> <p><sup>2</S.。你P.><span>阿卜杜勒阿齐兹国王大学数学系，邮编80203，沙特阿拉伯吉达21589</S.。P.一种N.></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">展示更多</B.。你T.T.O.N.> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</B.。GyD.F4.y2B.一种>Zeki Ayag.</D.一世v> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</S.。P.一种N.> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2008年10月10日</S.。P.一种N.> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</S.。P.一种N.> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2009年2月28日</S.。P.一种N.> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">公认</S.。P.一种N.> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2009年4月13日</S.。P.一种N.> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</S.。P.一种N.> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2009年6月21日</S.。P.一种N.> </div> </div> </div> <article class="sc-jtRlXQ bfymXb article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">抽象的</H4.> <p>摘要给出了Yalvac(1988)定义的模糊集的模糊半闭和模糊半内的几个性质，并给出了反例。研究了模糊半开集和模糊半闭集的刻画和性质。此外，我们定义了模糊s开映射和模糊s闭映射，并给出了一些有趣的刻画。</P.> <span class="end-abs"></span> <h4 id="introduction">1.介绍</H4.> <p>模糊集的概念是由Zadeh在他的经典论文[<一种HR.E.F=“#B31">1</一种>]．该概念为数学提供了自然的基础，用于在我们现实世界中普遍存在的模糊现象，以及建立模糊数学的新分支。在模糊拓扑领域，由chang介绍[<一种HR.E.F=“#B10">2</一种>，在模糊集合中推广一般拓扑的基本概念，形成了现代模糊拓扑理论。</P.> <p>近年来，人们发现模糊拓扑在解决许多实际问题中非常有用。Du等[<一种HR.E.F=“#B12">3.</一种>]模糊了成功的9个交叉口Egenhofer模型[<一种HR.E.F=“#B13">4.</一种>那<一种HR.E.F=“#B14">5.</一种>[描绘地理信息系统（GIS）查询中的拓扑关系。在 [<一种HR.E.F=“#B23">6.</一种>那<一种HR.E.F=“#B24">7.</一种>] El Naschie表明，模糊拓扑的概念可能与弦理论有关的量子颗粒物理和量子重力相关<S.。GyD.F4.y2B.一种vg height="11.25" id="M1" style="vertical-align:-0.13794pt;width:17.8375px;" version="1.1" viewbox="0 0 17.8375 11.25" width="17.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.25)"> <g transform="translate(72,-63)"> <text transform="matrix(1,0,0,-1,-71.95,63.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-66.39,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</T.。S.。P.一种N.> </text> </g> </g> </svg>理论。唐 [<一种HR.E.F=“#B28">8.</一种>]使用Chang的模糊拓扑空间略微改变，以模拟GIS数据库的空间对象和GIS的结构化查询语言（SQL）。</P.> <p>Levine [<一种HR.E.F=“#B21">9.</一种>介绍了拓扑空间中半开放和半连续映射的概念。有趣的是，他的工作在数字拓扑领域找到了应用程序[<一种HR.E.F=“#B25">10</一种>]．例如，发现数字线路是一个<S.。GyD.F4.y2B.一种vg height="14.3875" id="M2" style="vertical-align:-3.25793pt;width:23.325001px;" version="1.1" viewbox="0 0 23.325001 14.3875" width="23.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-65.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</T.。S.。P.一种N.> </text> </g> </g> </svg>-空间 [<一种HR.E.F=“#B9">11</一种>，这是一个较弱的基于半开集的分离公理。模糊数字拓扑[<一种HR.E.F=“#B26">12</一种>[Rosenfeld是由A. Rosenfeld介绍的，这表明需要模糊较弱的古典拓扑形式的概念。Azad [<一种HR.E.F=“#B5">13</一种>[1981年，在1981年进行了这种模糊化，并提出了一些模糊空间的一般性。已经讨论了模糊半开（RESP。，模糊半封闭），模糊常规开放（RESP。，封闭）集的几种属性。此外，他定义了模糊半连续（RESP。，半开和半闭合）功能，并研究了产品相关空间中的模糊半连续功能的特性。最后，他定义和表征了模糊几乎连续映射。对于相关后续工作，我们指的是[<一种HR.E.F=“#B1">14</一种>-<一种HR.E.F=“#B32">27</一种>]．</P.> <p>在本文中，我们的目标是进一步有助于研究由YALVAC定义的模糊半开和模糊半封闭套[<一种HR.E.F=“#B30">26</一种>]通过建立几个重要的基本身份和由反例支持的不平等。卡梅伦和伍兹[<一种HR.E.F=“#B8">28</一种>引入了s-连续映射和s-开映射的概念。他们研究了这些映射的性质以及它们与半开集性质的关系。汗和艾哈迈德[<一种HR.E.F=“#B18">29</一种>]进一步研究了S连续，S开和S闭映射的特征和性质。我们模糊了[<一种HR.E.F=“#B8">28</一种>那<一种HR.E.F=“#B18">29</一种>]．我们定义了模糊的S-OPEN和FUZZY S关闭映射，并建立了这些映射的一些有趣的特征。</P.> <h4 id="preliminaries">2.初步</H4.> <p>为了使本文自包含，我们简要回顾了某些定义和结果;对于那些未描述的，我们指的是[<一种HR.E.F=“#B31">1</一种>那<一种HR.E.F=“#B10">2</一种>那<一种HR.E.F=“#B5">13</一种>那<一种HR.E.F=“#B30">26</一种>]．</P.> <p>让<S.。GyD.F4.y2B.一种vg height="13.575" id="M3" style="vertical-align:-2.26974pt;width:55.462502px;" version="1.1" viewbox="0 0 55.462502 13.575" width="55.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.38253" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.259178" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>是一个点（物体）的空间，具有通用元素<S.。GyD.F4.y2B.一种vg height="7.1624999" id="M4" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．一个模糊的套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M5" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在<S.。GyD.F4.y2B.一种vg height="10.325" id="M6" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>以隶属函数为特征<S.。GyD.F4.y2B.一种vg height="13.45" id="M7" style="vertical-align:-2.21957pt;width:27.5875px;" version="1.1" viewbox="0 0 27.5875 13.45" width="27.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.764123" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.804272" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>从<S.。GyD.F4.y2B.一种vg height="10.325" id="M8" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>到单位区间<S.。GyD.F4.y2B.一种vg height="13.125" id="M9" style="vertical-align:-1.95624pt;width:32.674999px;" version="1.1" viewbox="0 0 32.674999 13.125" width="32.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> [</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.867746" y="0"> ]</T.。S.。P.一种N.> </text> </g> </g> </svg>．</P.> <p>象征<S.。GyD.F4.y2B.一种vg height="10.475" id="M10" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> φ.</T.。S.。P.一种N.> </text> </g> </g> </svg>表示定义为的空模糊组<S.。GyD.F4.y2B.一种vg height="14.6" id="M11" style="vertical-align:-3.13504pt;width:68.724998px;" version="1.1" viewbox="0 0 68.724998 14.6" width="68.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-64.34,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> φ.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-57.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.666979" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>对所有<S.。GyD.F4.y2B.一种vg height="10.75" id="M12" style="vertical-align:-0.33858pt;width:44.362499px;" version="1.1" viewbox="0 0 44.362499 10.75" width="44.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="32.25774" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>为了<S.。GyD.F4.y2B.一种vg height="10.325" id="M13" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，会员函数定义为<S.。GyD.F4.y2B.一种vg height="14.6" id="M14" style="vertical-align:-3.13504pt;width:65.775002px;" version="1.1" viewbox="0 0 65.775002 14.6" width="65.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-64.34,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-56.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.666979" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 1</T.。S.。P.一种N.> </text> </g> </g> </svg>,尽管<S.。GyD.F4.y2B.一种vg height="10.75" id="M15" style="vertical-align:-0.33858pt;width:41.387501px;" version="1.1" viewbox="0 0 41.387501 10.75" width="41.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</P.> <p><span class="statement" id="deff1"><span class="statement-title"><i class="statement-title">定义1（见[<一种HR.E.F=“#B10">2</一种>])。</一世></span>让<S.。GyD.F4.y2B.一种vg height="13.4875" id="M16" style="vertical-align:-2.34499pt;width:78.599998px;" version="1.1" viewbox="0 0 78.599998 13.4875" width="78.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，写作<S.。GyD.F4.y2B.一种vg height="16.775" id="M21" style="vertical-align:-2.34499pt;width:43.387501px;" version="1.1" viewbox="0 0 43.387501 16.775" width="43.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.12767" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>，是一个模糊的套装<S.。GyD.F4.y2B.一种vg height="10.325" id="M22" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>与隶属函数<S.。GyD.F4.y2B.一种vg height="13.45" id="M26" style="vertical-align:-2.21957pt;width:27.5875px;" version="1.1" viewbox="0 0 27.5875 13.45" width="27.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.764123" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.804272" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．图像的<S.。GyD.F4.y2B.一种vg height="10.8125" id="M27" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，写作<S.。GyD.F4.y2B.一种vg height="13.6125" id="M28" style="vertical-align:-2.34499pt;width:27.6625px;" version="1.1" viewbox="0 0 27.6625 13.6125" width="27.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>，是一个模糊的套装<S.。GyD.F4.y2B.一种vg height="10.325" id="M29" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>其成员函数是由<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq2"> <svg height="53.150002" id="M30" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 53.150002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,53.15)"> <g transform="translate(72,-29.48)"> <text transform="matrix(1,0,0,-1,67.07,47.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.740002" y="9.7299995"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.53" y="-0.0099999998"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.693499" y="-0.0099999998"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.457623" y="-0.0099999998"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.696619" y="-0.0099999998"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.860119" y="-0.0099999998"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; 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" x="7.2554078" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,175.14,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.841061" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.00456" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.88121" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.044708" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.134151" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.762901" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.238735" y="0"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.565735" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,249.15,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,262.11,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.767483" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.243317" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.282986" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="39.534485" y="0"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.785988" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.037487" y="0"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.588818" y="0"> M.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.291145" y="0"> P.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.530144" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.005974" y="0"> y</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="83.257477" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-123.85" y="26.940001"> 0.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-117.5985" y="26.940001"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-33.200001" y="26.940001"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-26.9485" y="26.940001"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-23.472666" y="26.940001"> H</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-17.221167" y="26.940001"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-11.669834" y="26.940001"> R.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-7.5063348" y="26.940001"> W.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="1.520831" y="26.940001"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.996665" y="26.940001"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.8603315" y="26.940001"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.411664" y="26.940001"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="212.00999" y="13.36"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="216.17349" y="13.36"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="222.425" y="13.36"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span>对所有<S.。GyD.F4.y2B.一种vg height="13.1875" id="M31" style="vertical-align:-2.29482pt;width:38.75px;" version="1.1" viewbox="0 0 38.75 13.1875" width="38.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.1875)"> <g transform="translate(72,-61.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.705208" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</S.。P.一种N.></p> <p><span class="statement" id="deff2"><span class="statement-title"><i class="statement-title">定义2(见[<一种HR.E.F=“#B10">2</一种>])。</一世></span>模糊拓扑是一个族<S.。GyD.F4.y2B.一种vg height="6.8874998" id="M32" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>的模糊集<S.。GyD.F4.y2B.一种vg height="10.325" id="M33" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，满足以下条件：<S.。P.一种N.CL.一种S.S.=“L.是T.“><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content"> <svg height="12.675" id="M34" style="vertical-align:-1.76814pt;width:62.637501px;" version="1.1" viewbox="0 0 62.637501 12.675" width="62.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.675)"> <g transform="translate(72,-61.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> φ.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.741037" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.09424" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.134628" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="46.536167" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content">如果<S.。GyD.F4.y2B.一种vg height="13.425" id="M35" style="vertical-align:-2.29482pt;width:52px;" version="1.1" viewbox="0 0 52 13.425" width="52" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.764123" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.965371" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.055532" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.095921" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，然后<S.。GyD.F4.y2B.一种vg height="16.1" id="M36" style="vertical-align:-3.2729pt;width:69.487503px;" version="1.1" viewbox="0 0 69.487503 16.1" width="69.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.8500004" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.48" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.57016" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.598045" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.999584" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span><span class="list-item"><span class="list-label">（3）</S.。P.一种N.><span class="list-content">如果<S.。GyD.F4.y2B.一种vg height="14.5875" id="M37" style="vertical-align:-3.2316pt;width:40px;" version="1.1" viewbox="0 0 40 14.5875" width="40" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-58.49,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>对于每一个人<S.。GyD.F4.y2B.一种vg height="10.75" id="M38" style="vertical-align:-0.33858pt;width:33.287498px;" version="1.1" viewbox="0 0 33.287498 10.75" width="33.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，然后<S.。GyD.F4.y2B.一种vg height="14.5875" id="M39" style="vertical-align:-3.2316pt;width:53.712502px;" version="1.1" viewbox="0 0 53.712502 14.5875" width="53.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∨</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-64.2,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-60.98,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-54.21,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-47.52,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</S.。P.一种N.></span></span></span></p> <p> <svg height="6.8874998" id="M40" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>被称为模糊拓扑<S.。GyD.F4.y2B.一种vg height="10.325" id="M41" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和这对<S.。GyD.F4.y2B.一种vg height="13.45" id="M42" style="vertical-align:-2.21957pt;width:37.400002px;" version="1.1" viewbox="0 0 37.400002 13.45" width="37.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.040869" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.242117" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>是一个fts。每个成员<S.。GyD.F4.y2B.一种vg height="6.8874998" id="M43" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>被称为<S.。GyD.F4.y2B.一种vg height="6.8874998" id="M44" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>-open fuzzy set（或只是一个开放的模糊集）。模糊套装是<S.。GyD.F4.y2B.一种vg height="6.8874998" id="M45" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>当且仅当它的补码为<S.。GyD.F4.y2B.一种vg height="6.8874998" id="M46" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>-打开。</P.> <p>与一般拓扑一样，不置于模糊拓扑仅包含<S.。GyD.F4.y2B.一种vg height="10.475" id="M47" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> φ.</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="10.325" id="M48" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，而离散模糊拓扑包含所有模糊集。</P.> <h4 id="fuzzy-semi-open-and-fuzzy-semi-closed-sets">3.模糊半开集和模糊半闭集</H4.> <p></p> <p><span class="statement" id="deff3"><span class="statement-title"><i class="statement-title">定义3(见[<一种HR.E.F=“#B5">13</一种>])。</一世></span>让<S.。GyD.F4.y2B.一种vg height="10.8125" id="M49" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中是一个模糊集<S.。GyD.F4.y2B.一种vg height="13.45" id="M50" style="vertical-align:-2.21957pt;width:37.400002px;" version="1.1" viewbox="0 0 37.400002 13.45" width="37.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.040869" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.242117" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．然后<S.。GyD.F4.y2B.一种vg height="10.8125" id="M51" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>的模糊半开集<S.。GyD.F4.y2B.一种vg height="10.325" id="M52" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，如果存在<S.。GyD.F4.y2B.一种vg height="8.8500004" id="M53" style="vertical-align:-0.33858pt;width:35.362499px;" version="1.1" viewbox="0 0 35.362499 8.8500004" width="35.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>这样<S.。GyD.F4.y2B.一种vg height="12.4125" id="M54" style="vertical-align:-1.29163pt;width:80.425003px;" version="1.1" viewbox="0 0 80.425003 12.4125" width="80.425003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="32.020184" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.060574" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.400074" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.951405" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．一个模糊的套装<S.。GyD.F4.y2B.一种vg height="9.6750002" id="M55" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>模糊半闭是否当且仅当它的补码<S.。GyD.F4.y2B.一种vg height="14.0625" id="M56" style="vertical-align:-2.29482pt;width:15.35px;" version="1.1" viewbox="0 0 15.35 14.0625" width="15.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-64.34,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半开的。所有模糊半开放式的类。，模糊半封闭)开始<S.。GyD.F4.y2B.一种vg height="10.325" id="M57" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>用来表示<S.。GyD.F4.y2B.一种vg height="13.45" id="M58" style="vertical-align:-2.21957pt;width:51.537498px;" version="1.1" viewbox="0 0 51.537498 13.45" width="51.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.903336" y="0"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.930502" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.094002" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.971371" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>(职责。<S.。GyD.F4.y2B.一种vg height="13.45" id="M59" style="vertical-align:-2.21957pt;width:50.6875px;" version="1.1" viewbox="0 0 50.6875 13.45" width="50.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.903336" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.242838" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.283707" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>）。</S.。P.一种N.></p> <p><span class="statement" id="deff4"><span class="statement-title"><i class="statement-title">定义4（见[<一种HR.E.F=“#B30">26</一种>])。</一世></span>让<S.。GyD.F4.y2B.一种vg height="10.8125" id="M60" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中是一个模糊集<S.。GyD.F4.y2B.一种vg height="10.325" id="M61" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．然后半闭合（简要<S.。GyD.F4.y2B.一种vg height="11.0125" id="M62" style="vertical-align:-0.17554pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 11.0125" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> </text> </g> </g> </svg>）和半室内（简要<S.。GyD.F4.y2B.一种vg height="10.625" id="M63" style="vertical-align:-0.12538pt;width:23.5625px;" version="1.1" viewbox="0 0 23.5625 10.625" width="23.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.625)"> <g transform="translate(72,-63.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> </text> </g> </g> </svg>）的<S.。GyD.F4.y2B.一种vg height="10.8125" id="M64" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>被定义为<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq3"> <svg height="41.349998" id="M65" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.35)"> <g transform="translate(72,-38.92)"> <text transform="matrix(1,0,0,-1,96.55,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.862206" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="56.863644" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.316154" y="0"> ∣</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.117783" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="84.357742" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.385628" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="103.3623" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="112.73955" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="123.89223" y="0"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="128.05573" y="0"> 你</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="134.30722" y="0"> Z.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="139.85855" y="0"> Z.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="145.4099" y="0"> y</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="154.78714" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="159.6508" y="0"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="165.20213" y="0"> M.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="174.92947" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="178.4053" y="0"> -</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="182.5688" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="188.12013" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="191.59598" y="0"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="197.84747" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="202.71114" y="0"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="208.26247" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="214.51398" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="222.59091" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-2.0799999" y="20.48"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="2.7836671" y="20.48"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.947166" y="20.48"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.198666" y="20.48"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.749998" y="20.48"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.989956" y="20.48"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.030342" y="20.48"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.869999" y="20.469999"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="56.871441" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.311447" y="20.469999"> ∣</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.113075" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="84.565582" y="20.469999"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.605972" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="103.37009" y="20.469999"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="112.74734" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="123.88752" y="20.469999"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="128.05103" y="20.469999"> 你</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="134.30252" y="20.469999"> Z.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="139.85385" y="20.469999"> Z.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="145.40518" y="20.469999"> y</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="154.78244" y="20.469999"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="159.6461" y="20.469999"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="165.19743" y="20.469999"> M.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="174.92476" y="20.469999"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="178.4006" y="20.469999"> -</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="182.5641" y="20.469999"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="188.8156" y="20.469999"> P.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="195.06709" y="20.469999"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="200.61842" y="20.469999"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="206.86993" y="20.469999"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="214.95937" y="20.469999"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="377.57001" y="10.86"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="381.73349" y="10.86"> 3.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="387.98499" y="10.86"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span>的模糊半闭包<S.。GyD.F4.y2B.一种vg height="10.8125" id="M66" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="12.175" id="M69" style="vertical-align:-1.29163pt;width:62.474998px;" version="1.1" viewbox="0 0 62.474998 12.175" width="62.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.175)"> <g transform="translate(72,-62.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; 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" x="48.411617" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.275284" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.614784" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.166115" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.406075" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.446465" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="94.310127" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="102.64963" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="108.20096" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>那<S.。GyD.F4.y2B.一种vg height="13.425" id="M71" style="vertical-align:-2.29482pt;width:89.587502px;" version="1.1" viewbox="0 0 89.587502 13.425" width="89.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.069956" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.110344" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.97401" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.137508" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.389011" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.940342" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</S.。P.一种N.></span></span> <p>我们都知道 [<一种HR.E.F=“#B5">13</一种>]一种模糊的套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M72" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M73" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是</P.> <span class="list"><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content">模糊半闭当且仅当<S.。GyD.F4.y2B.一种vg height="12.4125" id="M74" style="vertical-align:-1.29163pt;width:71.162498px;" version="1.1" viewbox="0 0 71.162498 12.4125" width="71.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.021622" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>(职责。<S.。GyD.F4.y2B.一种vg height="11.05" id="M75" style="vertical-align:-0.20064pt;width:59.875px;" version="1.1" viewbox="0 0 59.875 11.05" width="59.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>）;</S.。P.一种N.></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content">如果才能模糊半开<S.。GyD.F4.y2B.一种vg height="12.4125" id="M76" style="vertical-align:-1.29163pt;width:71.162498px;" version="1.1" viewbox="0 0 71.162498 12.4125" width="71.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.607344" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.083179" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.498177" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>(职责。<S.。GyD.F4.y2B.一种vg height="10.8125" id="M77" style="vertical-align:-0.20064pt;width:62.474998px;" version="1.1" viewbox="0 0 62.474998 10.8125" width="62.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.069956" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.110344" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>）。</S.。P.一种N.></span></span> <p>以下是模糊半封闭套装的特征，定理证明<一种HR.E.F=“#thm5">1</一种>很简单。</P.> <p><span class="statement" id="thm5"><span class="statement-title">定理1。</S.。P.一种N.><i>一个模糊的套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M78" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>如果才有模糊半关闭，只有在存在模糊关闭的封闭式套件时<S.。GyD.F4.y2B.一种vg height="9.875" id="M79" style="vertical-align:-2.29482pt;width:11.8625px;" version="1.1" viewbox="0 0 11.8625 9.875" width="11.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>这样<S.。GyD.F4.y2B.一种vg height="13.425" id="M80" style="vertical-align:-2.29482pt;width:94.712502px;" version="1.1" viewbox="0 0 94.712502 13.425" width="94.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.831919" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.872307" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.099762" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.140148" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.5299" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></p> <p><span class="statement" id="thm6"><span class="statement-title">定理2。</S.。P.一种N.><i>对于模糊套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M81" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M82" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>那<S.。GyD.F4.y2B.一种vg height="10.8125" id="M83" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>如果才有，如果才有模糊半关闭<S.。GyD.F4.y2B.一种vg height="12.4125" id="M84" style="vertical-align:-1.29163pt;width:83.324997px;" version="1.1" viewbox="0 0 83.324997 12.4125" width="83.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.618168" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.957668" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.508999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.789345" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</一世></span></p> <p><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</一世></span> <svg height="13.45" id="M85" style="vertical-align:-2.21957pt;width:29.35px;" version="1.1" viewbox="0 0 29.35 13.45" width="29.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⇒</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.204609" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>如果<S.。GyD.F4.y2B.一种vg height="14.2" id="M86" style="vertical-align:-2.7337pt;width:287.96249px;" version="1.1" viewbox="0 0 287.96249 14.2" width="287.96249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.403456" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.392874" y="0"> 一种</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.069956" y="0"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.233456" y="0"> 你</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.484955" y="0"> Z.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.036285" y="0"> Z.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.58762" y="0"> y</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.964867" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.828537" y="0"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.379868" y="0"> M.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="82.107201" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="85.583038" y="0"> -</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.746536" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="95.297867" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="98.773697" y="0"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="105.0252" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="109.88887" y="0"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="115.4402" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="124.81745" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="129.68112" y="0"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="135.13243" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="138.60826" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="144.84726" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="148.42311" y="0"> H</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="154.67461" y="0"> 一种</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="160.22595" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="166.82753" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="170.30336" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="175.16702" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="182.45628" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="192.69624" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="204.73662" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="209.6003" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="217.93979" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="223.49112" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，然后<S.。GyD.F4.y2B.一种vg height="12.4125" id="M87" style="vertical-align:-1.29163pt;width:137.21249px;" version="1.1" viewbox="0 0 137.21249 12.4125" width="137.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.618168" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.957668" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.508999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.789345" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.653015" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.816513" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.068008" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="80.619347" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="90.859299" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="102.89969" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．<B.。R.> <svg height="13.45" id="M88" style="vertical-align:-2.21957pt;width:29.35px;" version="1.1" viewbox="0 0 29.35 13.45" width="29.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⇐</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.204609" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>认为<S.。GyD.F4.y2B.一种vg height="13.5625" id="M89" style="vertical-align:-2.21957pt;width:93.724998px;" version="1.1" viewbox="0 0 93.724998 13.5625" width="93.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.672501" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.436623" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="56.075954" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.116341" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．自从<S.。GyD.F4.y2B.一种vg height="11.05" id="M90" style="vertical-align:-0.20064pt;width:32.037498px;" version="1.1" viewbox="0 0 32.037498 11.05" width="32.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半封闭的，所以存在一个封闭的套装<S.。GyD.F4.y2B.一种vg height="9.875" id="M91" style="vertical-align:-2.29482pt;width:11.8625px;" version="1.1" viewbox="0 0 11.8625 9.875" width="11.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>这样<S.。GyD.F4.y2B.一种vg height="13.6625" id="M92" style="vertical-align:-2.29482pt;width:114.25px;" version="1.1" viewbox="0 0 114.25 13.6625" width="114.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6625)"> <g transform="translate(72,-61.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.831919" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.872307" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.735973" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.075474" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.626808" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.86676" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.90715" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．因此<S.。GyD.F4.y2B.一种vg height="13.6625" id="M93" style="vertical-align:-2.29482pt;width:216.83749px;" version="1.1" viewbox="0 0 216.83749 13.6625" width="216.83749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6625)"> <g transform="translate(72,-61.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.831919" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.872307" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.735973" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="49.899471" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="56.150974" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.626808" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.490471" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.829971" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="78.38131" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.621262" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="100.66165" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="110.90161" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="122.9295" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="127.79316" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="136.13266" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="141.6965" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="151.93646" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="163.97685" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>或<S.。GyD.F4.y2B.一种vg height="13.425" id="M94" style="vertical-align:-2.29482pt;width:90.800003px;" version="1.1" viewbox="0 0 90.800003 13.425" width="90.800003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.831919" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.872307" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.099762" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.140148" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．因此<S.。GyD.F4.y2B.一种vg height="10.8125" id="M95" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半封闭的<S.。GyD.F4.y2B.一种vg height="11.05" id="M96" style="vertical-align:-0.20064pt;width:59.875px;" version="1.1" viewbox="0 0 59.875 11.05" width="59.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.13151" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.471012" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</S.。P.一种N.></p> <p><span class="statement" id="rem7"><span class="statement-title"><i class="statement-title">备注1。</一世></span>很容易看出<S.。P.一种N.CL.一种S.S.=“L.是T.“><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content">如果<S.。GyD.F4.y2B.一种vg height="10.8125" id="M97" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半开放(对应。那F你Z.Z.yS.E.M.一世-CL.O.S.E.D.), then<S.vg height="13" id="M98" style="vertical-align:-1.76814pt;width:118.4px;" version="1.1" viewbox="0 0 118.4 13" width="118.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13)"> <g transform="translate(72,-61.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.730453" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="32.107704" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.971371" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.134869" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.386372" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.950207" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.714329" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.091576" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.955246" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="82.294746" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.846077" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>,<S.。GyD.F4.y2B.一种vg height="11.05" id="M99" style="vertical-align:-0.20064pt;width:25.950001px;" version="1.1" viewbox="0 0 25.950001 11.05" width="25.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半开（RESP。，模糊半封闭）;</S.。P.一种N.></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content">一个非偏离的模糊套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M100" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半闭而不是模糊半开。</S.。P.一种N.></span></span></span></p> <p>与Remark相反<一种HR.E.F=“#rem7">1</一种>（2）通常是如下所示的。</P.> <p><span class="statement" id="ex8"><span class="statement-title"><i class="statement-title">例1。</一世></span>让<S.。GyD.F4.y2B.一种vg height="13.575" id="M101" style="vertical-align:-2.26974pt;width:81.5625px;" version="1.1" viewbox="0 0 81.5625 13.575" width="81.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; 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" x="82.732353" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.983849" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>为中模糊集的隶属度等级格<S.。GyD.F4.y2B.一种vg height="10.325" id="M103" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．让<S.。GyD.F4.y2B.一种vg height="14.8125" id="M104" style="vertical-align:-3.25793pt;width:214.8875px;" version="1.1" viewbox="0 0 214.8875 14.8125" width="214.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; 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" x="2.188" y="0"> 3.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,127.67,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>那<S.。GyD.F4.y2B.一种vg height="14.8125" id="M111" style="vertical-align:-3.25793pt;width:346.47501px;" version="1.1" viewbox="0 0 346.47501 14.8125" width="346.47501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-59.67,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.61,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-41.52,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-36.65,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-26.25,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 3.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-19.19,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.204128" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,4.3,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,11.36,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,22.45,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,27.32,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,37.72,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,44.78,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.204128" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,68.27,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,75.33,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,86.42,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,93.48,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,103.88,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,110.94,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.204128" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,134.43,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,141.5,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,152.58,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,159.64,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,170.04,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,174.92,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.080057" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.081497" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>计算给出了这种模糊套装<S.。GyD.F4.y2B.一种vg height="7.1875" id="M112" style="vertical-align:-0.13794pt;width:10.7625px;" version="1.1" viewbox="0 0 10.7625 7.1875" width="10.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>既是模糊半封闭和模糊半开，但是<S.。GyD.F4.y2B.一种vg height="11.0125" id="M113" style="vertical-align:-0.17554pt;width:79.449997px;" version="1.1" viewbox="0 0 79.449997 11.0125" width="79.449997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="39.772041" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.812431" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.326977" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></span></p> <p><span class="statement" id="thm9"><span class="statement-title">定理3。</S.。P.一种N.><i>用于模糊套<S.。GyD.F4.y2B.一种vg height="10.8125" id="M114" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="9.6750002" id="M115" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M116" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，一个有</一世><span class="list"><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content"><i> <svg height="13.55" id="M117" style="vertical-align:-2.29482pt;width:192.41251px;" version="1.1" viewbox="0 0 192.41251 13.55" width="192.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.716751" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.705688" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.869186" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.408978" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.949005" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="55.563332" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.190163" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.230553" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="80.731873" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="86.733315" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="92.947304" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="98.948746" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="108.48853" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="119.01606" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="124.51738" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="130.51881" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="136.7328" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="142.73425" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="150.34857" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content"><i> <svg height="16.1" id="M118" style="vertical-align:-3.2729pt;width:195.83749px;" version="1.1" viewbox="0 0 195.83749 16.1" width="195.83749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="34.639999" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="108.13" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.716751" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.63019" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.79369" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.279999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="55.881824" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.521156" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.561546" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.062866" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.064308" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="93.278297" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="99.279739" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="121.77" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="127.27132" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="133.27277" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="139.48676" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="145.47569" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="153.09001" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（3）</S.。P.一种N.><span class="list-content"><i> <svg height="13.55" id="M119" style="vertical-align:-2.29482pt;width:176.325px;" version="1.1" viewbox="0 0 176.325 13.55" width="176.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.030287" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.570074" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="42.097603" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="49.711929" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.351261" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.37915" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.88047" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="83.269981" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.583992" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="99.123787" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="109.66381" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="115.16513" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="123.55465" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="129.85616" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="137.47049" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（4）</S.。P.一种N.><span class="list-content"><i> <svg height="16.1" id="M120" style="vertical-align:-3.2729pt;width:181.91251px;" version="1.1" viewbox="0 0 181.91251 16.1" width="181.91251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="30.879999" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="100.85" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.030287" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.52" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.121822" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.761158" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="71.801544" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.302864" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="85.692383" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="91.993889" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="114.49" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="119.99132" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="128.38083" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="134.68234" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="142.29668" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span></span><i></i></span></p> <p><span class="statement" id="proof2"><span class="statement-title"><i class="statement-title">证明。</一世></span>（1）<S.。GyD.F4.y2B.一种vg height="10.8125" id="M121" style="vertical-align:-0.20064pt;width:34.625px;" version="1.1" viewbox="0 0 34.625 10.8125" width="34.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.325" id="M122" style="vertical-align:-2.29482pt;width:35.6875px;" version="1.1" viewbox="0 0 35.6875 13.325" width="35.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.325)"> <g transform="translate(72,-61.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>都是模糊半开。<S.。GyD.F4.y2B.一种vg height="13.425" id="M123" style="vertical-align:-2.29482pt;width:137.8125px;" version="1.1" viewbox="0 0 137.8125 13.425" width="137.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.807632" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="42.335159" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="49.949486" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.326736" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="70.416893" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="82.457283" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="91.99707" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="102.5246" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>意味着<S.。GyD.F4.y2B.一种vg height="13.55" id="M124" style="vertical-align:-2.29482pt;width:122.475px;" version="1.1" viewbox="0 0 122.475 13.55" width="122.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.069956" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.110344" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.97401" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.137508" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.389011" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.864845" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.028343" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.56813" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="86.095657" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="93.709984" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.55" id="M125" style="vertical-align:-2.29482pt;width:123.5375px;" version="1.1" viewbox="0 0 123.5375 13.55" width="123.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.920158" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.960548" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.824215" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.987713" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.239216" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.71505" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.878548" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="76.418335" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="86.945862" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="94.560188" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．结合，<S.。GyD.F4.y2B.一种vg height="13.55" id="M126" style="vertical-align:-2.29482pt;width:174.675px;" version="1.1" viewbox="0 0 174.675 13.55" width="174.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.369787" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.909817" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.773483" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="49.936981" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="56.18848" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.739815" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.829971" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="84.870361" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.734032" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="93.89753" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="100.14903" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="103.62486" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="107.78836" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="117.32816" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="127.85567" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="135.47" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>或<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq4"> <svg height="22.799999" id="M127" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 22.799999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.8)"> <g transform="translate(72,-53.76)"> <text transform="matrix(1,0,0,-1,132.61,59.75)"> <tspan style="font-size: 12.50px; " x="102.05" y="6.5500002"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.533287" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.073315" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.687641" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.314472" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.354858" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.218529" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.382027" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.63353" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="93.197365" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="119.95" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="124.81367" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="128.97717" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="135.22867" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="140.78" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="148.39432" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="341.51001" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="345.67349" y="0"> 4.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="351.92499" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span><br>（2）<S.。GyD.F4.y2B.一种vg height="16.1" id="M128" style="vertical-align:-3.2729pt;width:65.587502px;" version="1.1" viewbox="0 0 65.587502 16.1" width="65.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.8500004" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.48" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.57016" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.598045" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="16.1" id="M129" style="vertical-align:-3.2729pt;width:66.650002px;" version="1.1" viewbox="0 0 66.650002 16.1" width="66.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.8500004" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.48" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.57016" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.598045" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>意味着<S.。GyD.F4.y2B.一种vg height="16.1" id="M130" style="vertical-align:-3.2729pt;width:184.6125px;" version="1.1" viewbox="0 0 184.6125 16.1" width="184.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="31.77" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="102.38" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.400002" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.014328" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.65366" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.681549" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.545212" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.70871" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.960213" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="93.524048" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="116.01" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="120.87366" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="125.03716" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="131.28867" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="136.85251" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="144.46683" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>反过来<S.。GyD.F4.y2B.一种vg height="12.175" id="M131" style="vertical-align:-1.29163pt;width:62.474998px;" version="1.1" viewbox="0 0 62.474998 12.175" width="62.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.175)"> <g transform="translate(72,-62.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.069956" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.110344" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.325" id="M132" style="vertical-align:-2.29482pt;width:64.599998px;" version="1.1" viewbox="0 0 64.599998 13.325" width="64.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.325)"> <g transform="translate(72,-61.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.920158" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.960548" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>意味着<S.。GyD.F4.y2B.一种vg height="16.1" id="M133" style="vertical-align:-3.2729pt;width:146.8625px;" version="1.1" viewbox="0 0 146.8625 16.1" width="146.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="29.690001" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.129997" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="109.77" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.32" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.183666" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.347164" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.598667" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.150002" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.240158" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.280548" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="16.1" id="M134" style="vertical-align:-3.2729pt;width:89.849998px;" version="1.1" viewbox="0 0 89.849998 16.1" width="89.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="29.690001" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.32" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.183666" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.347164" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.598667" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.150002" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半开的。但<S.。GyD.F4.y2B.一种vg height="16.1" id="M135" style="vertical-align:-3.2729pt;width:71.599998px;" version="1.1" viewbox="0 0 71.599998 16.1" width="71.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="31.77" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.400002" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.014328" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>最大模糊半开集是这样的吗<S.。GyD.F4.y2B.一种vg height="16.1" id="M136" style="vertical-align:-3.2729pt;width:132.52499px;" version="1.1" viewbox="0 0 132.52499 16.1" width="132.52499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="31.77" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.540001" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.400002" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.014328" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.65366" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.681549" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="95.18" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="102.78182" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>因此<S.。GyD.F4.y2B.一种vg height="16.1" id="M137" style="vertical-align:-3.2729pt;width:184.6125px;" version="1.1" viewbox="0 0 184.6125 16.1" width="184.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="29.690001" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="119.05" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.32" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.183666" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.347164" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.598667" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.150002" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.240158" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.280548" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="92.144218" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.307716" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="102.55921" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="106.03505" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="110.19855" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="132.69" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="140.29182" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="144.45532" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>这给出了平等。<B.。R.> <svg height="13.45" id="M138" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 3.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.45" id="M139" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>轻松遵循<S.。GyD.F4.y2B.一种vg height="13.45" id="M140" style="vertical-align:-2.21957pt;width:22.25px;" version="1.1" viewbox="0 0 22.25 13.45" width="22.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></span></p> <p>不平等<S.。GyD.F4.y2B.一种vg height="13.45" id="M141" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.45" id="M142" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>的定理<一种HR.E.F=“#thm9">3.</一种>，一般不可逆转，如下所示。</P.> <p><span class="statement" id="ex10"><span class="statement-title"><i class="statement-title">例2。</一世></span>让<S.。GyD.F4.y2B.一种vg height="13.575" id="M143" style="vertical-align:-2.26974pt;width:68.5625px;" version="1.1" viewbox="0 0 68.5625 13.575" width="68.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.38253" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="42.872787" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.749195" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>是一套<S.。GyD.F4.y2B.一种vg height="13.7" id="M144" style="vertical-align:-2.26974pt;width:82.387497px;" version="1.1" viewbox="0 0 82.387497 13.7" width="82.387497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7)"> <g transform="translate(72,-61.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.4647713" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.505159" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.506599" y="0"> 0.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.758099" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.971851" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="42.097603" y="0"> 5.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.349102" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.55035" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.801849" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>成为模糊套装的成员级别的格子<S.。GyD.F4.y2B.一种vg height="10.325" id="M145" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．让<S.。GyD.F4.y2B.一种vg height="14.8125" id="M146" style="vertical-align:-3.25793pt;width:171.2375px;" version="1.1" viewbox="0 0 171.2375 14.8125" width="171.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; 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" x="25.118526" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.160355" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,35.92,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,42.98,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,54.07,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,58.94,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>,<S.。GyD.F4.y2B.一种vg height="14.8125" id="M147" style="vertical-align:-3.25793pt;width:81.787498px;" version="1.1" viewbox="0 0 81.787498 14.8125" width="81.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="6.8874998" id="M149" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>产生的模糊拓扑<S.。GyD.F4.y2B.一种vg height="9.6750002" id="M150" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>那<S.。GyD.F4.y2B.一种vg height="7.2375002" id="M151" style="vertical-align:-0.11285pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.2375)"> <g transform="translate(72,-66.21)"> <text transform="matrix(1,0,0,-1,-71.95,66.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>,<S.。GyD.F4.y2B.一种vg height="7.1875" id="M152" style="vertical-align:-0.13794pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 7.1875" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.5145426" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>然后<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq5"> <svg height="19.35" id="M153" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,103.85,61.13)"> <tspan style="font-size: 12.50px; " x="21.92" y="2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.889999" y="2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.080002" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.110001" y="0"> φ.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.649788" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.851036" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.465363" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="56.679115" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.95562" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.156868" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="76.67141" y="0"> 那</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,199.21,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,206.27,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,217.35,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,224.42,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.2700005" y="-2.51"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.48" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.67" y="-2.51"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,252.37,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,257.24,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,268.33,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,275.39,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.110001" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.2700005" y="-2.51"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.471248" y="-2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.380001" y="-2.51"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="198.73" y="-2.51"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="202.89349" y="-2.51"> 5.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="209.145" y="-2.51"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span>我们选择模糊套装<S.。GyD.F4.y2B.一种vg height="14.8125" id="M154" style="vertical-align:-3.25793pt;width:262.08749px;" version="1.1" viewbox="0 0 262.08749 14.8125" width="262.08749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.556852" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-37.11,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-30.05,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-18.96,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-14.09,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.37869" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.831198" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.859085" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.860523" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,36.06,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,40.93,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,52.02,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,59.08,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.366187" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.193544" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.235374" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,108.6,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,115.66,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,126.75,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,131.62,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="14.8125" id="M155" style="vertical-align:-3.25793pt;width:82.912498px;" version="1.1" viewbox="0 0 82.912498 14.8125" width="82.912498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.7523403" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.792728" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.794168" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-37.87,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-33,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-21.91,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-14.85,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>然后计算给出<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq6"> <svg height="50.9375" id="M156" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.9375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.9375)"> <g transform="translate(72,-31.25)"> <text transform="matrix(1,0,0,-1,80.89,60.67)"> <tspan style="font-size: 12.50px; " x="72.019997" y="2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="79.199997" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.833359" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.360886" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.337559" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.976891" y="0"> =</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,166.37,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,173.43,60.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,184.52,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,191.58,58.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.73" y="-5.5100002"> ̸</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.2799997" y="-2.51"> <</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.92" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.110001" y="-2.51"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,224.97,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,229.84,60.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,240.93,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,247.99,58.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-95.080002" y="24.809999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-87.900002" y="22.299999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.66" y="-2.51"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.70039" y="-2.51"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.564056" y="-2.51"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.727554" y="-2.51"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.979053" y="-2.51"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.530388" y="-2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.370247" y="-2.51"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.897774" y="-2.51"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.761444" y="-2.51"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.924942" y="-2.51"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="79.176437" y="-2.51"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="84.727776" y="-2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="91.704445" y="-2.51"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-174.07001" y="22.299999"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-169.20633" y="22.299999"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-160.86684" y="22.299999"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-155.31551" y="22.299999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-146.18831" y="22.299999"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-135.64828" y="22.299999"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-130.78461" y="22.299999"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-122.44511" y="22.299999"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-116.89378" y="22.299999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-107.12894" y="22.299999"> =</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,166.37,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,171.25,35.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,182.33,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,189.39,33.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.73" y="-5.52"> ̸</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.2799997" y="-2.51"> <</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.93" y="-7.1054274e-015"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.110001" y="-2.51"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,222.78,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,229.84,35.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,240.93,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,247.99,33.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.66" y="-2.51"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.70039" y="-2.51"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.564056" y="-2.51"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.903557" y="-2.51"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.459999" y="-2.52"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.623501" y="-2.52"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.75069" y="-2.52"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.278214" y="-2.52"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="71.567223" y="-2.52"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.818726" y="-2.52"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="226.13" y="-15.15"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="230.2935" y="-15.15"> 6.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="236.545" y="-15.15"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span></p> <p>我们都知道 [<一种HR.E.F=“#B27">30.</一种>]对于模糊套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M157" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="12.5375" id="M158" style="vertical-align:-1.76814pt;width:16.375px;" version="1.1" viewbox="0 0 16.375 12.5375" width="16.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.5375)"> <g transform="translate(72,-61.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>我们有</P.> <span class="list"><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content"> <svg height="13" id="M159" style="vertical-align:-1.76814pt;width:96.362503px;" version="1.1" viewbox="0 0 96.362503 13" width="96.362503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13)"> <g transform="translate(72,-61.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.815335" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.679003" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.018503" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.569836" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.809792" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.850182" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.189682" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.741013" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.505135" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content"> <svg height="12.4125" id="M160" style="vertical-align:-1.29163pt;width:98.525002px;" version="1.1" viewbox="0 0 98.525002 12.4125" width="98.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.021622" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.925678" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.265179" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.816513" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.580635" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span></span> <p>我们使用这个和定理<一种HR.E.F=“#thm5">1</一种>，并证明以下内容。</P.> <p><span class="statement" id="thm11"><span class="statement-title">定理4。</S.。P.一种N.><i>让<S.。GyD.F4.y2B.一种vg height="10.8125" id="M161" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中是一个模糊集<S.。GyD.F4.y2B.一种vg height="10.325" id="M162" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．然后会有如下结果:</一世><span class="list"><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content"><i> <svg height="13.45" id="M163" style="vertical-align:-2.21957pt;width:243.71249px;" version="1.1" viewbox="0 0 243.71249 13.45" width="243.71249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.368107" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.059132" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.299088" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.339478" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.840797" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.230309" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="78.206268" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="84.97039" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.133888" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="94.635208" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="100.63665" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="106.85064" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="110.76408" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="116.2654" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="122.26684" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="128.48083" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="134.46977" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="144.70972" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="156.75011" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="162.25143" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="168.25287" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="174.46686" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="180.46831" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="187.23242" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="191.39592" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content"><i> <svg height="12.7625" id="M164" style="vertical-align:-1.76814pt;width:131.58749px;" version="1.1" viewbox="0 0 131.58749 12.7625" width="131.58749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.7625)"> <g transform="translate(72,-61.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.716751" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.63019" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.13151" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.521023" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.822536" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.062492" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.102882" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="70.104324" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="76.318314" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="80.23175" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.621262" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="94.922775" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="101.6869" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（3）</S.。P.一种N.><span class="list-content"><i> <svg height="12.7625" id="M165" style="vertical-align:-1.76814pt;width:151.75px;" version="1.1" viewbox="0 0 151.75 12.7625" width="151.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.7625)"> <g transform="translate(72,-61.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.215431" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.12887" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.63019" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.63163" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.845619" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.75906" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.26038" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.649895" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.951405" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.19136" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="80.23175" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="86.233192" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="92.447182" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.360619" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="104.75014" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="111.05164" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="117.81577" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（4）</S.。P.一种N.><span class="list-content"><i> <svg height="12.175" id="M166" style="vertical-align:-1.29163pt;width:156.25px;" version="1.1" viewbox="0 0 156.25 12.175" width="156.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.175)"> <g transform="translate(72,-62.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.716751" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.63019" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.13151" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.521023" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.822536" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.062492" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.102882" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="70.104324" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="76.318314" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="80.23175" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.621262" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="94.922775" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="104.47507" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="115.00259" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="121.76672" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span></span><i></i></span></p> <p><span class="statement" id="proof3"><span class="statement-title"><i class="statement-title">证明。</一世></span> <svg height="13.45" id="M167" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>事实是<S.。GyD.F4.y2B.一种vg height="11.05" id="M168" style="vertical-align:-0.20064pt;width:32.037498px;" version="1.1" viewbox="0 0 32.037498 11.05" width="32.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>模糊半封闭，那<S.。GyD.F4.y2B.一种vg height="10.8125" id="M169" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>如果才有，如果才有模糊半关闭<S.。GyD.F4.y2B.一种vg height="11.05" id="M170" style="vertical-align:-0.20064pt;width:59.875px;" version="1.1" viewbox="0 0 59.875 11.05" width="59.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，它立即跟随。<B.。R.> <svg height="13.45" id="M171" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>自从，<S.。GyD.F4.y2B.一种vg height="12.4125" id="M172" style="vertical-align:-1.29163pt;width:94.612503px;" version="1.1" viewbox="0 0 94.612503 12.4125" width="94.612503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.021622" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.925678" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.265179" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.816513" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>,所以<S.。GyD.F4.y2B.一种vg height="12.4125" id="M173" style="vertical-align:-1.29163pt;width:118.0625px;" version="1.1" viewbox="0 0 118.0625 12.4125" width="118.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.021622" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.925678" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.089176" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.340675" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.816513" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.680176" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="82.019676" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.571014" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，由于所有模糊开放套装都是模糊的半开。<B.。R.> <svg height="13.45" id="M174" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 3.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>经过<S.。GyD.F4.y2B.一种vg height="13.45" id="M175" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>那<S.。GyD.F4.y2B.一种vg height="12.4125" id="M176" style="vertical-align:-1.29163pt;width:118.0625px;" version="1.1" viewbox="0 0 118.0625 12.4125" width="118.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.021622" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.925678" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.089176" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.340675" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.816513" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.680176" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="82.019676" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.571014" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>,所以<S.。GyD.F4.y2B.一种vg height="12.4125" id="M177" style="vertical-align:-1.29163pt;width:135.425px;" version="1.1" viewbox="0 0 135.425 12.4125" width="135.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.021622" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.22551" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.477013" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.952847" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.816513" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.980011" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="79.231514" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="82.707344" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.571014" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="95.910515" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="101.46185" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．还<S.。GyD.F4.y2B.一种vg height="12.4125" id="M178" style="vertical-align:-1.29163pt;width:77.25px;" version="1.1" viewbox="0 0 77.25 12.4125" width="77.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="49.374348" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.925678" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>,所以<S.。GyD.F4.y2B.一种vg height="12.4125" id="M179" style="vertical-align:-1.29163pt;width:100.7px;" version="1.1" viewbox="0 0 100.7 12.4125" width="100.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.618168" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.957668" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.508999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.789345" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.128845" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.680176" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="12.4125" id="M180" style="vertical-align:-1.29163pt;width:139.325px;" version="1.1" viewbox="0 0 139.325 12.4125" width="139.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.169498" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="32.645332" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.508999" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.848499" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.399834" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.63979" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.680176" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.843681" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="84.095177" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.571014" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="95.910515" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="101.46185" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="108.22597" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>因此，我们得到了<S.。GyD.F4.y2B.一种vg height="13.45" id="M181" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 3.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．<B.。R.> <svg height="13.45" id="M182" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>现在<S.。GyD.F4.y2B.一种vg height="12.4125" id="M183" style="vertical-align:-1.29163pt;width:176.21249px;" version="1.1" viewbox="0 0 176.21249 12.4125" width="176.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.021622" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.22551" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.477013" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.952847" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.292343" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.843681" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.395973" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="97.923492" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="108.16345" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="120.19134" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="128.53084" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="134.09468" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>通过定理<一种HR.E.F=“#thm5">1</一种>那<S.。GyD.F4.y2B.一种vg height="11.25" id="M184" style="vertical-align:-0.36366pt;width:68.412498px;" version="1.1" viewbox="0 0 68.412498 11.25" width="68.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.25)"> <g transform="translate(72,-63)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.230333" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.321453" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.861485" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>模糊半封闭。还<S.。GyD.F4.y2B.一种vg height="12.4125" id="M185" style="vertical-align:-1.29163pt;width:96.25px;" version="1.1" viewbox="0 0 96.25 12.4125" width="96.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.431341" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="32.682842" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.158676" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.498177" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.601803" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="70.129326" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．自从<S.。GyD.F4.y2B.一种vg height="11.05" id="M186" style="vertical-align:-0.20064pt;width:32.037498px;" version="1.1" viewbox="0 0 32.037498 11.05" width="32.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>最小模糊半闭集为<S.。GyD.F4.y2B.一种vg height="12.4125" id="M187" style="vertical-align:-1.29163pt;width:59.875px;" version="1.1" viewbox="0 0 59.875 12.4125" width="59.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.13151" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.471012" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，所以，<S.。GyD.F4.y2B.一种vg height="12.4125" id="M188" style="vertical-align:-1.29163pt;width:119.7125px;" version="1.1" viewbox="0 0 119.7125 12.4125" width="119.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.198345" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.449844" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.925678" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="63.265179" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="68.816513" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="78.368805" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.896332" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．这意味着<S.。GyD.F4.y2B.一种vg height="12.4125" id="M189" style="vertical-align:-1.29163pt;width:194.45px;" version="1.1" viewbox="0 0 194.45 12.4125" width="194.45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4125)"> <g transform="translate(72,-62.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.618168" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.957668" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.508999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.789345" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.653015" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.992516" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="78.543846" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.783806" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="100.82419" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="104.98769" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="111.23919" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="114.71503" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; 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" x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,7.02,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊集<S.。GyD.F4.y2B.一种vg height="12.5375" id="M199" style="vertical-align:-1.76814pt;width:16.375px;" version="1.1" viewbox="0 0 16.375 12.5375" width="16.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.5375)"> <g transform="translate(72,-61.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="6.8874998" id="M200" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>产生的模糊拓扑<S.。GyD.F4.y2B.一种vg height="9.6750002" id="M201" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>那<S.。GyD.F4.y2B.一种vg height="7.2375002" id="M202" style="vertical-align:-0.11285pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.2375)"> <g transform="translate(72,-66.21)"> <text transform="matrix(1,0,0,-1,-71.95,66.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>,<S.。GyD.F4.y2B.一种vg height="7.1875" id="M203" style="vertical-align:-0.13794pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 7.1875" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.5145426" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>然后<S.。GyD.F4.y2B.一种vg height="14.8125" id="M204" style="vertical-align:-3.25793pt;width:254.41251px;" version="1.1" viewbox="0 0 254.41251 14.8125" width="254.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.8648672" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.905256" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.906696" y="0"> φ.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.446484" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="42.660236" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.274563" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="55.475811" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.752316" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.966064" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.480614" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="80.694359" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="86.695801" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,21.03,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,25.9,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,36.99,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,44.05,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,54.45,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,61.51,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.204128" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,85,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,89.87,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,100.96,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,108.02,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,118.42,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 3.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,125.48,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>那<S.。GyD.F4.y2B.一种vg height="14.8125" id="M205" style="vertical-align:-3.25793pt;width:339.83749px;" version="1.1" viewbox="0 0 339.83749 14.8125" width="339.83749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-59.67,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 3.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.61,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-41.52,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-34.46,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-24.06,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 3.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-17,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.204128" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,6.49,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,13.55,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,24.64,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,29.51,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,39.91,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,46.97,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.204128" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,70.46,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 3.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,77.52,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,88.61,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,95.67,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,106.07,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,110.94,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.204128" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,134.43,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,141.5,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,152.58,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,157.46,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,167.85,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,172.73,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.080057" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>．<B.。R.>我们选择模糊套装<S.。GyD.F4.y2B.一种vg height="14.8125" id="M206" style="vertical-align:-3.25793pt;width:104.1625px;" version="1.1" viewbox="0 0 104.1625 14.8125" width="104.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.269283" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-37.4,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-30.33,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-19.25,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-12.19,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-1.79,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,5.27,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="14.8125" id="M207" style="vertical-align:-3.25793pt;width:101.9625px;" version="1.1" viewbox="0 0 101.9625 14.8125" width="101.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.853084" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.893473" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.894913" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-34.77,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-29.9,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-18.81,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-13.94,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-3.54,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,3.52,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> </text> </g> </g> </svg>，然后计算给出<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq7"> <svg height="50.9375" id="M208" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.9375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.9375)"> <g transform="translate(72,-31.25)"> <text transform="matrix(1,0,0,-1,89.28,60.67)"> <tspan style="font-size: 12.50px; " x="59.799999" y="2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.989998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.618168" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.957668" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.508999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> =</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,162.54,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 7.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,169.6,60.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,180.69,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,187.75,60.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,198.15,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,205.21,58.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.73" y="-5.5100002"> ̸</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.2799997" y="-2.51"> <</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.92" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.110001" y="-2.51"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,238.6,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,243.47,60.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,254.56,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,261.62,60.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,272.02,57.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,279.08,58.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-130" y="24.809999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-122.81" y="22.299999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.67" y="-2.51"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.697886" y="-2.51"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.861385" y="-2.51"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.112885" y="-2.51"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.588718" y="-2.51"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.928219" y="-2.51"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.492054" y="-2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.25618" y="-2.51"> ;</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-205.39" y="22.299999"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-201.2265" y="22.299999"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-194.97501" y="22.299999"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-191.49916" y="22.299999"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-183.15967" y="22.299999"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-177.60834" y="22.299999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-165.44292" y="22.299999"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-154.91539" y="22.299999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-142.0498" y="22.299999"> =</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,162.54,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,167.42,35.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,178.5,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,183.38,35.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,193.77,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="2.188" y="0"> 5.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,200.84,33.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.73" y="-5.52"> ̸</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.2700005" y="-2.51"> <</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.92" y="-7.1054274e-015"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.110001" y="-2.51"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,234.22,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,239.1,35.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,250.18,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,255.06,35.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,265.46,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,270.33,33.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.66" y="-2.51"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.70039" y="-2.51"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.564056" y="-2.51"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.727554" y="-2.51"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.979053" y="-2.51"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.454887" y="-2.51"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="46.318558" y="-2.51"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.658058" y="-2.51"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.209389" y="-2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.599144" y="-2.51"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="203.78999" y="-15.15"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="207.95351" y="-15.15"> 7.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="214.205" y="-15.15"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span></p> <p><span class="statement" id="thm13"><span class="statement-title">定理5。</S.。P.一种N.><i>对于任何模糊集<S.。GyD.F4.y2B.一种vg height="10.8125" id="M209" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M210" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，我们有</一世><span class="list"><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content"><i> <svg height="14.175" id="M211" style="vertical-align:-2.21957pt;width:120.6375px;" version="1.1" viewbox="0 0 120.6375 14.175" width="120.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.175)"> <g transform="translate(72,-60.66)"> <text transform="matrix(1,0,0,-1,-71.95,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.666259" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.880251" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.869186" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.633308" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-33.14,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-25.1,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.529205" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.894672" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.05817" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,15.73,67.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,20.3,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>那</一世></span></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content"><i> <svg height="14.175" id="M212" style="vertical-align:-2.21957pt;width:120.95px;" version="1.1" viewbox="0 0 120.95 14.175" width="120.95" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.175)"> <g transform="translate(72,-60.66)"> <text transform="matrix(1,0,0,-1,-71.95,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.355844" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.119967" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-36.66,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-28.62,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.54171" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.54315" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.757139" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.670578" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.83408" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,15.98,67.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,20.55,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．</一世></span></span></span><i></i></span></p> <p><span class="statement" id="proof4"><span class="statement-title"><i class="statement-title">证明。</一世></span>（<S.。GyD.F4.y2B.一种vg height="10.6875" id="M213" style="vertical-align:-0.0pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 10.6875" width="7.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</T.。S.。P.一种N.> </text> </g> </g> </svg>的）<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq8"> <svg height="146.9875" id="M214" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 146.9875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,146.9875)"> <g transform="translate(72,45.59)"> <text transform="matrix(1,0,0,-1,87.59,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.442165" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,123.52,68.09)"> <tspan style="font-size: 8.75px; 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" x="42.247639" y="20.469999"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.249077" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.339237" y="20.469999"> ∣</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.128365" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.218529" y="20.469999"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.258919" y="20.469999"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.210587" y="20.469999"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="103.16225" y="20.469999"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="114.27742" y="20.469999"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="118.44092" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="129.06847" y="20.469999"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="139.48347" y="20.469999"> 一种</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="145.03481" y="20.469999"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="151.2863" y="20.469999"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="161.70129" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="172.79146" y="20.469999"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="184.81935" y="20.469999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="191.58347" y="20.469999"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="40.950001"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.040389" y="40.950001"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.879999" y="40.939999"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.881439" y="40.939999"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.908607" y="40.939999"> −</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.248829" y="40.939999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="59.338989" y="40.939999"> ∣</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.12812" y="40.939999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.218277" y="40.939999"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="89.258667" y="40.939999"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.210335" y="40.939999"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="103.162" y="40.939999"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="114.27717" y="40.939999"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="118.44067" y="40.939999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="129.06822" y="40.939999"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="139.48322" y="40.939999"> 一种</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="145.03455" y="40.939999"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="151.28606" y="40.939999"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="161.70105" y="40.939999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="172.79121" y="40.939999"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="184.81909" y="40.939999"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="191.58322" y="40.939999"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="62.59"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.040389" y="62.59"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.867746" y="62.59"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.869186" y="62.59"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.734776" y="62.59"> ∣</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.536407" y="62.59"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,188.49,5.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,196.53,0.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.931223" y="0"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.046391" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.209888" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.837437" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.252438" y="0"> 一种</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.803772" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.055267" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="84.470268" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="97.335854" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="109.37624" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,312.68,5.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,317.25,0.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> 那</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-103.48" y="20.48"> W.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-94.452835" y="20.48"> H</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-88.201332" y="20.48"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-82.650002" y="20.48"> R.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-78.486504" y="20.48"> E.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-68.771675" y="20.48"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-55.906086" y="20.48"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-43.878201" y="20.48"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-34.838531" y="20.48"> −</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-23.498308" y="20.48"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-185.69" y="42.119999"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-173.64961" y="42.119999"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-168.78595" y="42.119999"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-160.44644" y="42.119999"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-154.89511" y="42.119999"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-150.73161" y="42.119999"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,173.29,-36.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,177.86,-41.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.238997" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="296.26001" y="-51.869999"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="300.42349" y="-51.869999"> 8.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="306.67499" y="-51.869999"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span><br> <svg height="13.45" id="M215" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>类似于<S.。GyD.F4.y2B.一种vg height="13.45" id="M216" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．</S.。P.一种N.></p> <h4 id="fuzzy-s-open-and-fuzzy-s-closed-mappings">4.模糊的S-OPEN和FUZZY S封闭映射</H4.> <p>首先，我们定义</P.> <p><span class="statement" id="deff14"><span class="statement-title"><i class="statement-title">定义5。</一世></span>一个功能<S.。GyD.F4.y2B.一种vg height="13.4875" id="M217" style="vertical-align:-2.34499pt;width:78.599998px;" version="1.1" viewbox="0 0 78.599998 13.4875" width="78.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ∶</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.267363" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.446243" y="0"> →</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.587856" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>被认为是模糊的s-open(对应。那F你Z.Z.yS.-CL.O.S.E.D.的）如果 the image of every fuzzy semi-open (resp., fuzzy semi-closed) set is fuzzy open (resp., fuzzy closed).</S.P.一种N.></p> <p>显然，一个模糊s开函数是模糊开的。</P.> <p><span class="statement" id="deff15"><span class="statement-title"><i class="statement-title">定义6（见[<一种HR.E.F=“#B22">31</一种>])。</一世></span>模糊点<S.。GyD.F4.y2B.一种vg height="7.1875" id="M218" style="vertical-align:-0.13794pt;width:7.0749998px;" version="1.1" viewbox="0 0 7.0749998 7.1875" width="7.0749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>被称为模糊集的边界点<S.。GyD.F4.y2B.一种vg height="10.8125" id="M219" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>如果，只有<S.。GyD.F4.y2B.一种vg height="16.1" id="M220" style="vertical-align:-3.2729pt;width:103.4875px;" version="1.1" viewbox="0 0 103.4875 16.1" width="103.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="43.82" y="0.029999999"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.067554" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.407057" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.97089" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.459999" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.7995" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="71.35083" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,6.17,67.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．所有边界点的联盟<S.。GyD.F4.y2B.一种vg height="10.8125" id="M221" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>被称为边界<S.。GyD.F4.y2B.一种vg height="10.8125" id="M222" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，表示<S.。GyD.F4.y2B.一种vg height="11.05" id="M223" style="vertical-align:-0.20064pt;width:29.424999px;" version="1.1" viewbox="0 0 29.424999 11.05" width="29.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．很清楚<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq9"> <svg height="15.975" id="M224" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 15.975" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.975)"> <g transform="translate(72,-59.22)"> <text transform="matrix(1,0,0,-1,157.74,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.934341" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.273842" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.837677" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.377468" y="0"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.917496" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.256996" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="86.808327" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,251.32,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,255.89,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="218.23" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="222.39349" y="0"> 9.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="228.645" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span></p> <p>接下来,我们定义</P.> <p><span class="statement" id="deff16"><span class="statement-title"><i class="statement-title">定义7。</一世></span>半葡萄干（简短的SBD）模糊套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M225" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M226" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>被定义为<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq10"> <svg height="15.975" id="M227" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 15.975" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.975)"> <g transform="translate(72,-59.22)"> <text transform="matrix(1,0,0,-1,150.44,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.530167" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.770123" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.810513" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.674179" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.01368" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.565014" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.117302" y="0"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="82.644829" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="87.508499" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="95.848" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="101.41183" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,258.62,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,263.19,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="204.67999" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="208.84351" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="215.095" y="0"> 0.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="221.3465" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span></p> <p>在下文中，我们在SINT，SCL和SBD方面表征了模糊的S-OPEN映射。</P.> <p><span class="statement" id="thm17"><span class="statement-title">定理6。</S.。P.一种N.><i>对于一个功能<S.。GyD.F4.y2B.一种vg height="13.4875" id="M228" style="vertical-align:-2.34499pt;width:78.599998px;" version="1.1" viewbox="0 0 78.599998 13.4875" width="78.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ∶</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.267363" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.446243" y="0"> →</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.587856" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，一个模糊的套装<S.。GyD.F4.y2B.一种vg height="7.1750002" id="M229" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M230" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和一个模糊集<S.。GyD.F4.y2B.一种vg height="13.425" id="M231" style="vertical-align:-2.29482pt;width:8.8500004px;" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="12.5375" id="M232" style="vertical-align:-1.76814pt;width:12.3875px;" version="1.1" viewbox="0 0 12.3875 12.5375" width="12.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.5375)"> <g transform="translate(72,-61.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>那么下面是等价的:</一世><span class="list"><span class="list-item"><span class="list-label">（1）</S.。P.一种N.><span class="list-content"><i> <svg height="13.4875" id="M233" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊的s开;</一世></span></span><span class="list-item"><span class="list-label">（2）</S.。P.一种N.><span class="list-content"><i> <svg height="13.6125" id="M234" style="vertical-align:-2.34499pt;width:125.675px;" version="1.1" viewbox="0 0 125.675 13.6125" width="125.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.932661" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.984352" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="46.623688" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.664078" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.827576" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.079079" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.630409" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.569572" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="85.73307" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="92.78476" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.948265" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（3）</S.。P.一种N.><span class="list-content"><i> <svg height="16.775" id="M235" style="vertical-align:-2.34499pt;width:156.41251px;" version="1.1" viewbox="0 0 156.41251 16.775" width="156.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-42.67,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-31.8,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.12767" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.767002" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.807392" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,7.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,18.32,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.106504" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.270002" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（4）</S.。P.一种N.><span class="list-content"><i> <svg height="16.775" id="M236" style="vertical-align:-2.34499pt;width:159.02499px;" version="1.1" viewbox="0 0 159.02499 16.775" width="159.02499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.503" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="32.670338" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.710728" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="49.574394" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.389729" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.55323" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,21.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,32.22,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.140173" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.303672" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.467171" y="0"> ;</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span><span class="list-item"><span class="list-label">（5）</S.。P.一种N.><span class="list-content"><i> <svg height="16.775" id="M237" style="vertical-align:-2.34499pt;width:173.325px;" version="1.1" viewbox="0 0 173.325 16.775" width="173.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.503" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.88217" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.685001" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.725391" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.589058" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="66.928558" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="73.180061" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="77.343559" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,33.15,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,44.02,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.12767" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.291169" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></span></span><i></i></span></p> <p><span class="statement" id="proof5"><span class="statement-title"><i class="statement-title">证明。</一世></span> <svg height="13.45" id="M238" style="vertical-align:-2.21957pt;width:59.724998px;" version="1.1" viewbox="0 0 59.724998 13.45" width="59.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ⇒</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.09544" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.258942" y="0"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.510441" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>明显地<S.。GyD.F4.y2B.一种vg height="13.6125" id="M239" style="vertical-align:-2.34499pt;width:101.3625px;" version="1.1" viewbox="0 0 101.3625 13.6125" width="101.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.932661" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.984352" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="46.623688" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.664078" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="65.603241" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.766739" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="76.818436" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．<S.。GyD.F4.y2B.一种vg height="13.4875" id="M240" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>模糊S-OPEN给出<S.。GyD.F4.y2B.一种vg height="13.6125" id="M241" style="vertical-align:-2.34499pt;width:54.075001px;" version="1.1" viewbox="0 0 54.075001 13.6125" width="54.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.932661" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.984352" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>这是模糊的开放<S.。GyD.F4.y2B.一种vg height="10.325" id="M242" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．但<S.。GyD.F4.y2B.一种vg height="13.6125" id="M243" style="vertical-align:-2.34499pt;width:47.987499px;" version="1.1" viewbox="0 0 47.987499 13.6125" width="47.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.905497" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.068995" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.120686" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>最大模糊开集是这样的吗<S.。GyD.F4.y2B.一种vg height="13.6125" id="M244" style="vertical-align:-2.34499pt;width:95.275002px;" version="1.1" viewbox="0 0 95.275002 13.6125" width="95.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.905497" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.068995" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.120686" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="41.760021" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.800407" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.739574" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="64.903076" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="71.954765" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．所以<S.。GyD.F4.y2B.一种vg height="13.6125" id="M245" style="vertical-align:-2.34499pt;width:125.2375px;" version="1.1" viewbox="0 0 125.2375 13.6125" width="125.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.932661" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.984352" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="46.623688" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.664078" y="0"> 一世</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.827576" y="0"> N.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.079079" y="0"> T.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.630409" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.569572" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="85.73307" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="92.78476" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="96.948265" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>对于任何模糊套装<S.。GyD.F4.y2B.一种vg height="7.1750002" id="M246" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在<S.。GyD.F4.y2B.一种vg height="10.325" id="M247" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．这给了<S.。GyD.F4.y2B.一种vg height="13.45" id="M248" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．<B.。R.> <svg height="13.45" id="M249" style="vertical-align:-2.21957pt;width:59.724998px;" version="1.1" viewbox="0 0 59.724998 13.45" width="59.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ⇒</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.09544" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.258942" y="0"> 3.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.510441" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>对于任何模糊集<S.。GyD.F4.y2B.一种vg height="13.425" id="M250" style="vertical-align:-2.29482pt;width:8.8500004px;" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>是一个模糊的封闭套装<S.。GyD.F4.y2B.一种vg height="10.325" id="M273" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．现在<S.。GyD.F4.y2B.一种vg height="17.9375" id="M274" style="vertical-align:-3.2729pt;width:230.2625px;" version="1.1" viewbox="0 0 230.2625 17.9375" width="230.2625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9375)"> <g transform="translate(72,-57.65)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.503" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.806671" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.446007" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.486393" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,3.29,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,14.16,60.96)"> <tspan style="font-size: 12.50px; " x="31.280001" y="0.02"> ⋀</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.919998" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.503" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,67.52,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,78.39,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.503" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,103.43,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,108,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．使用<S.。GyD.F4.y2B.一种vg height="13.45" id="M275" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>我们有<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq13"> <svg height="19.5625" id="M276" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.5625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.5625)"> <g transform="translate(72,-56.35)"> <text transform="matrix(1,0,0,-1,100.16,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,108.6,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,121.55,60.97)"> <tspan style="font-size: 12.50px; " x="66.260002" y="2.52"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="72.110001" y="0.0099999998"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.503" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.842501" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.819176" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="35.446007" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="47.486393" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="52.35006" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="60.689564" y="0"> L.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,202.1,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,215.05,60.97)"> <tspan style="font-size: 12.50px; " x="48.57" y="2.52"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="54.419998" y="0.0099999998"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.140173" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.267122" y="0"> ∧</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.807152" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="34.670818" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="43.010319" y="0"> L.</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,277.91,66.03)"> <tspan style="font-size: 8.75px; 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" x="15.31" y="2.52"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.140173" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,267.98,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,276.02,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.891554" y="0"> B.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.231054" y="0"> D.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="33.570557" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,318.04,65.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,330.99,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.12767" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="136.88" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="141.0435" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="147.295" y="0"> 4.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="153.54649" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span>这给了<S.。GyD.F4.y2B.一种vg height="13.6375" id="M278" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.6375" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 5.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．</S.。P.一种N.></p> <p>下面，我们给出模糊s-闭映射的刻画。</P.> <p><span class="statement" id="thm18"><span class="statement-title">定理7。</S.。P.一种N.><i>一个功能<S.。GyD.F4.y2B.一种vg height="13.4875" id="M279" style="vertical-align:-2.34499pt;width:78.599998px;" version="1.1" viewbox="0 0 78.599998 13.4875" width="78.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ∶</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.267363" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.446243" y="0"> →</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.587856" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>模糊s闭是否当且仅当<S.。GyD.F4.y2B.一种vg height="13.725" id="M280" style="vertical-align:-2.34499pt;width:115.4125px;" version="1.1" viewbox="0 0 115.4125 13.725" width="115.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="39.396954" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.437344" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.376507" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.540005" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.403671" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.743172" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.294502" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.058632" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>，每个模糊套装<S.。GyD.F4.y2B.一种vg height="10.8125" id="M281" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M282" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</一世></span></p> <p><span class="statement" id="proof6"><span class="statement-title"><i class="statement-title">证明。</一世></span> <svg height="13.45" id="M283" style="vertical-align:-2.21957pt;width:29.35px;" version="1.1" viewbox="0 0 29.35 13.45" width="29.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⇒</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.204609" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>明显地<S.。GyD.F4.y2B.一种vg height="13.725" id="M284" style="vertical-align:-2.34499pt;width:98.037498px;" version="1.1" viewbox="0 0 98.037498 13.725" width="98.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.534004" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.473171" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.636669" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.500336" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="61.839836" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.403671" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="74.167793" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．<S.。GyD.F4.y2B.一种vg height="13.725" id="M285" style="vertical-align:-2.34499pt;width:51.112499px;" version="1.1" viewbox="0 0 51.112499 13.725" width="51.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.305832" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.857164" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.621288" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>模糊关闭，自从<S.。GyD.F4.y2B.一种vg height="13.4875" id="M286" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊s-closed。但<S.。GyD.F4.y2B.一种vg height="13.725" id="M287" style="vertical-align:-2.34499pt;width:45.037498px;" version="1.1" viewbox="0 0 45.037498 13.725" width="45.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>是最小的模糊关闭设置<S.。GyD.F4.y2B.一种vg height="13.725" id="M288" style="vertical-align:-2.34499pt;width:91.962502px;" version="1.1" viewbox="0 0 91.962502 13.725" width="91.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.534004" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="45.873508" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.437344" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.376507" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.540005" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.304131" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．所以<S.。GyD.F4.y2B.一种vg height="13.725" id="M289" style="vertical-align:-2.34499pt;width:115.4125px;" version="1.1" viewbox="0 0 115.4125 13.725" width="115.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="39.396954" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.437344" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.376507" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.540005" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.403671" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.743172" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.294502" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.058632" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．<B.。R.> <svg height="13.45" id="M290" style="vertical-align:-2.21957pt;width:29.35px;" version="1.1" viewbox="0 0 29.35 13.45" width="29.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⇐</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.204609" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>让<S.。GyD.F4.y2B.一种vg height="13.45" id="M291" style="vertical-align:-2.21957pt;width:78.525002px;" version="1.1" viewbox="0 0 78.525002 13.45" width="78.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> F</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="29.219511" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.171181" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="44.510681" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="48.674179" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.551548" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．我们展示了这一点<S.。GyD.F4.y2B.一种vg height="13.6125" id="M292" style="vertical-align:-2.34499pt;width:27.6625px;" version="1.1" viewbox="0 0 27.6625 13.6125" width="27.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>模糊关闭。通过假设，<S.。GyD.F4.y2B.一种vg height="13.725" id="M293" style="vertical-align:-2.34499pt;width:162.33749px;" version="1.1" viewbox="0 0 162.33749 13.725" width="162.33749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="39.396954" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.437344" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.376507" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.540005" y="0"> S.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="67.403671" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="75.743172" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="81.294502" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="88.058632" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="95.69796" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="107.73835" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="114.67751" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="118.84102" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="125.60514" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>或<S.。GyD.F4.y2B.一种vg height="13.725" id="M294" style="vertical-align:-2.34499pt;width:91.962502px;" version="1.1" viewbox="0 0 91.962502 13.725" width="91.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> L.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="39.396954" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="51.437344" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="58.376507" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="62.540005" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="69.304131" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>．这证明了这一点<S.。GyD.F4.y2B.一种vg height="13.6125" id="M295" style="vertical-align:-2.34499pt;width:27.6625px;" version="1.1" viewbox="0 0 27.6625 13.6125" width="27.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>模糊关闭。</S.。P.一种N.></p> <p><span class="statement" id="thm19"><span class="statement-title">定理8。</S.。P.一种N.><i>如果是一个功能<S.。GyD.F4.y2B.一种vg height="13.4875" id="M296" style="vertical-align:-2.34499pt;width:78.599998px;" version="1.1" viewbox="0 0 78.599998 13.4875" width="78.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ∶</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.267363" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.446243" y="0"> →</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.587856" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>对于每个模糊集，模糊s是闭的吗<S.。GyD.F4.y2B.一种vg height="13.425" id="M297" style="vertical-align:-2.29482pt;width:8.8500004px;" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M298" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>每个模糊半开星<S.。GyD.F4.y2B.一种vg height="9.6750002" id="M299" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在FTS中<S.。GyD.F4.y2B.一种vg height="10.325" id="M300" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="16.775" id="M301" style="vertical-align:-2.34499pt;width:72.300003px;" version="1.1" viewbox="0 0 72.300003 16.775" width="72.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.118048" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-40.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-29.52,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.140173" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>时，存在一个模糊开集<S.。GyD.F4.y2B.一种vg height="7.2375002" id="M302" style="vertical-align:-0.11285pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.2375)"> <g transform="translate(72,-66.21)"> <text transform="matrix(1,0,0,-1,-71.95,66.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在<S.。GyD.F4.y2B.一种vg height="10.325" id="M303" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.425" id="M304" style="vertical-align:-2.29482pt;width:36.075001px;" version="1.1" viewbox="0 0 36.075001 13.425" width="36.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>这样<S.。GyD.F4.y2B.一种vg height="16.775" id="M305" style="vertical-align:-2.34499pt;width:71.425003px;" version="1.1" viewbox="0 0 71.425003 16.775" width="71.425003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.066835" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.107224" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．</一世></span></p> <p><span class="statement" id="proof7"><span class="statement-title"><i class="statement-title">证明。</一世></span>让<S.。GyD.F4.y2B.一种vg height="9.6750002" id="M306" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是一个任意模糊半开放式套装<S.。GyD.F4.y2B.一种vg height="10.325" id="M307" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="16.775" id="M308" style="vertical-align:-2.34499pt;width:72.300003px;" version="1.1" viewbox="0 0 72.300003 16.775" width="72.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.118048" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-40.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-29.52,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.140173" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>，在哪里<S.。GyD.F4.y2B.一种vg height="13.425" id="M309" style="vertical-align:-2.29482pt;width:8.8500004px;" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是一个模糊的套装<S.。GyD.F4.y2B.一种vg height="10.325" id="M310" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．清楚地<S.。GyD.F4.y2B.一种vg height="14.85" id="M311" style="vertical-align:-2.34499pt;width:77.787498px;" version="1.1" viewbox="0 0 77.787498 14.85" width="77.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.85)"> <g transform="translate(72,-60.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.266163" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-49.07,67.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-44.5,62.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-36.17,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-28.13,62.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>(说)是模糊开放的<S.。GyD.F4.y2B.一种vg height="10.325" id="M312" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．自从<S.。GyD.F4.y2B.一种vg height="16.775" id="M313" style="vertical-align:-2.34499pt;width:76.199997px;" version="1.1" viewbox="0 0 76.199997 16.775" width="76.199997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.12767" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.767002" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.807392" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="38.421719" y="0"> 那</T.。S.。P.一种N.> </text> </g> </g> </svg>然后简单的计算给出了这一点<S.。GyD.F4.y2B.一种vg height="13.425" id="M314" style="vertical-align:-2.29482pt;width:36.075001px;" version="1.1" viewbox="0 0 36.075001 13.425" width="36.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="22.480394" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．而且，我们有<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq15"> <svg height="79.537498" id="M315" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 79.537498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,79.5375)"> <g transform="translate(72,-8.37)"> <text transform="matrix(1,0,0,-1,146.84,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,155.28,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,168.23,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.066835" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.107224" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,206.78,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,217.65,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.266163" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,240.53,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,245.1,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,253.43,66.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,186.31,36.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.03" y="2.51"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.889999" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,212.63,41.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,223.5,36.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,242.22,41.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,246.79,36.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1599998" y="2.51"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,256.8,44.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,264.85,36.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-132.60001" y="24.51"> O.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-126.3485" y="24.51"> R.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="-118.0215" y="24.51"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,155.28,17.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,168.23,12.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.066835" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.107224" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.72155" y="0"> ．</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="299.64001" y="-24.889999"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="303.8035" y="-24.889999"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="310.05499" y="-24.889999"> 5.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="316.30649" y="-24.889999"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span></span></p> <p><span class="statement" id="thm20"><span class="statement-title">定理9。</S.。P.一种N.><i>让<S.。GyD.F4.y2B.一种vg height="13.4875" id="M316" style="vertical-align:-2.34499pt;width:78.599998px;" version="1.1" viewbox="0 0 78.599998 13.4875" width="78.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ∶</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.267363" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.446243" y="0"> →</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="53.587856" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是来自FTS的一个手术功能<S.。GyD.F4.y2B.一种vg height="10.325" id="M317" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>一个罚球<S.。GyD.F4.y2B.一种vg height="10.5" id="M318" style="vertical-align:-0.13794pt;width:12.3875px;" version="1.1" viewbox="0 0 12.3875 10.5" width="12.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5)"> <g transform="translate(72,-63.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg>对于每个模糊集<S.。GyD.F4.y2B.一种vg height="13.425" id="M319" style="vertical-align:-2.29482pt;width:8.8500004px;" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在<S.。GyD.F4.y2B.一种vg height="10.325" id="M320" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>每个模糊半开星<S.。GyD.F4.y2B.一种vg height="9.6750002" id="M321" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在<S.。GyD.F4.y2B.一种vg height="10.325" id="M322" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="16.775" id="M323" style="vertical-align:-2.34499pt;width:72.300003px;" version="1.1" viewbox="0 0 72.300003 16.775" width="72.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.118048" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-40.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-29.52,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.140173" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>时，存在一个模糊开集<S.。GyD.F4.y2B.一种vg height="7.2375002" id="M324" style="vertical-align:-0.11285pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.2375)"> <g transform="translate(72,-66.21)"> <text transform="matrix(1,0,0,-1,-71.95,66.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在<S.。GyD.F4.y2B.一种vg height="10.325" id="M325" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.425" id="M326" style="vertical-align:-2.29482pt;width:36.075001px;" version="1.1" viewbox="0 0 36.075001 13.425" width="36.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>这样<S.。GyD.F4.y2B.一种vg height="16.775" id="M327" style="vertical-align:-2.34499pt;width:71.425003px;" version="1.1" viewbox="0 0 71.425003 16.775" width="71.425003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.066835" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.107224" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>，然后<S.。GyD.F4.y2B.一种vg height="13.4875" id="M328" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>s-closed。</一世></span></p> <p><span class="statement" id="proof8"><span class="statement-title"><i class="statement-title">证明。</一世></span>让<S.。GyD.F4.y2B.一种vg height="9.875" id="M329" style="vertical-align:-2.29482pt;width:11.8625px;" version="1.1" viewbox="0 0 11.8625 9.875" width="11.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是一个任意模糊的半封闭套装<S.。GyD.F4.y2B.一种vg height="10.325" id="M330" style="vertical-align:-0.0pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="14.3375" id="M331" style="vertical-align:-2.34499pt;width:74.199997px;" version="1.1" viewbox="0 0 74.199997 14.3375" width="74.199997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.705208" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.868708" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="32.807873" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.971371" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="50.524624" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-17.25,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．然后<S.。P.一种N.CL.一种S.S.=“E.quation" id="eq16"> <svg height="20.2875" id="M332" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.2875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.2875)"> <g transform="translate(72,-55.77)"> <text transform="matrix(1,0,0,-1,101.62,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,110.06,65.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,123.01,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,161.49,65.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,172.36,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.266163" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.655916" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.819414" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,205.35,65.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,213.39,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.04" y="2.52"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.889999" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,239.72,65.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,250.59,60.39)"> <tspan style="font-size: 12.50px; " x="24.65" y="2.52"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.479914" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,281.09,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,289.13,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,310.56,65.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,467.87,60.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 6.</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg></span>或<S.。GyD.F4.y2B.一种vg height="16.775" id="M333" style="vertical-align:-2.34499pt;width:79.262497px;" version="1.1" viewbox="0 0 79.262497 16.775" width="79.262497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="17.991817" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-13.21,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．自从<S.。GyD.F4.y2B.一种vg height="14.0625" id="M334" style="vertical-align:-2.29482pt;width:17.575001px;" version="1.1" viewbox="0 0 17.575001 14.0625" width="17.575001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-62.56,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是模糊半开的，因此存在模糊开放式套装<S.。GyD.F4.y2B.一种vg height="13" id="M335" style="vertical-align:-4.74141pt;width:14.025px;" version="1.1" viewbox="0 0 14.025 13" width="14.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13)"> <g transform="translate(72,-61.6)"> <text transform="matrix(1,0,0,-1,-71.95,66.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-65.67,63.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="14.3375" id="M336" style="vertical-align:-4.74141pt;width:41.162498px;" version="1.1" viewbox="0 0 41.162498 14.3375" width="41.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,65.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.705208" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-43.96,62.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>这样<S.。GyD.F4.y2B.一种vg height="19.762501" id="M337" style="vertical-align:-4.74141pt;width:85.400002px;" version="1.1" viewbox="0 0 85.400002 19.762501" width="85.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.7625)"> <g transform="translate(72,-56.19)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-42.2,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-37.36,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-8.3,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．自从<S.。GyD.F4.y2B.一种vg height="13.4875" id="M338" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>是满射吗<S.。GyD.F4.y2B.一种vg height="17.325001" id="M339" style="vertical-align:-4.74141pt;width:107.4875px;" version="1.1" viewbox="0 0 107.4875 17.325001" width="107.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.325)"> <g transform="translate(72,-58.14)"> <text transform="matrix(1,0,0,-1,-71.95,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.705208" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-43.96,59.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-35.65,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="23.13055" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="27.294048" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="36.683804" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="40.847301" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,9.37,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>．因此<S.。GyD.F4.y2B.一种vg height="17.325001" id="M340" style="vertical-align:-4.74141pt;width:191.96249px;" version="1.1" viewbox="0 0 191.96249 17.325001" width="191.96249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.325)"> <g transform="translate(72,-58.14)"> <text transform="matrix(1,0,0,-1,-71.95,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="15.266163" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="24.643414" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="28.806911" y="0"> 的）</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-38.97,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-30.93,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> ∨</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> {</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="25.79369" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,1.14,59.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,9.45,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.8016319" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="16.466452" y="0"> ∈</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>或<S.。GyD.F4.y2B.一种vg height="13.6125" id="M342" style="vertical-align:-2.34499pt;width:30.950001px;" version="1.1" viewbox="0 0 30.950001 13.6125" width="30.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="20.479914" y="0"> 的）</T.。S.。P.一种N.> </text> </g> </g> </svg>模糊关闭<S.。GyD.F4.y2B.一种vg height="10.325" id="M343" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>在<S.。GyD.F4.y2B.一种vg height="10.325" id="M352" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>和<S.。GyD.F4.y2B.一种vg height="13.425" id="M353" style="vertical-align:-2.29482pt;width:36.075001px;" version="1.1" viewbox="0 0 36.075001 13.425" width="36.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> ≥</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> </T.。S.。P.一种N.> </text> </g> </g> </svg>这样<S.。GyD.F4.y2B.一种vg height="16.775" id="M354" style="vertical-align:-2.34499pt;width:75.324997px;" version="1.1" viewbox="0 0 75.324997 16.775" width="75.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.。S.。P.一种N.> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</T.。S.。P.一种N.> </text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> 的）</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="18.066835" y="0"> ≤</T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="30.107224" y="0"> </T.。S.。P.一种N.> <tspan style="font-size: 12.50px; " x="37.72155" y="0"> ．</T.。S.。P.一种N.> </text> </g> </g> </svg></i></span></p> </div> <div class="xml-content"> <h4 class="references" id="references">参考文献</H4.> <ol> <li id="B31">l.a. 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Ahmad和Athar Kharal。这是分布下的开放式访问文章<一种R.E.L.=“L.一世CE.N.S.E.“HR.ef="http://creativecommons.org/licenses/by/3.0/">创意公共归因许可证</一种>如果正确引用了原始工作，则允许在任何媒体中进行无限制使用，分发和再现。</P.> </div> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 becpDt hrTitleRef">更多相关文章</H4.> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 bvnCfh"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-cBdUnI hRnXob article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-exkUMo hymroZ pdf_desktop button__group" href="https://downloads.hindawi.com/journals/afs/2009/303042.pdf" aria-label="" target="_blank" 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height="24"><span class="text">下载引用</S.。P.一种N.></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-BngTV hmDWcT ref_desktop" href="//www.newsama.com/journals/afs/2009/303042.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" 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height="24"><span class="text">引用</S.。P.一种N.></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cTjmhe ihmyEq article_bottom_toolbar"> <div class="sc-cugefK itFKcQ accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</S.。P.一种N.><span class="sc-gkFcWv gWTCXQ">更多的</S.。P.一种N.></span> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/afs/2009/303042.xml" aria-label="XML" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> XML</D.一世v><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">订单印刷副本</S.。P.一种N.><span class="sc-gkFcWv gWTCXQ">命令</S.。P.一种N.></span><span class="sc-htoDjs kNoiZu sc-gbOuXE jGPvPL right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-hBbWxd kdRRST"> <div class="sc-dyGzUR cHatnS"> <div> 的观点<S.。P.一种N.>4610.</S.。P.一种N.> </div> <div> 下载<S.。P.一种N.>2105</S.。P.一种N.> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2009/303042" data-style="small_circle"></span>引用</D.一世v> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享帖子</H3.> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2009/303042&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" 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