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1、一类模糊蕴涵的研究摘要本文主要是对一类模糊蕴涵及其推广的性质进行了详细研究，其研究工作归纳如下：首先，我们对模糊蕴涵及其统一模的目前的相关研究进行了综述•主要内容包括三类模糊蕴涵(S蕴涵、R蕴涵、QL蕴涵)和由统一模生成的模糊蕴涵及算子性质的详细研究以及对这些蕴涵及算子的刻画•然后，我们简要介绍了模糊逻辑联结(非，八模，一余模，模糊蕴涵)的相关概念.其次，我们对It^的性质进行详细研究•讨论了Zr.v满足常见的模糊蕴涵性质的条件；给出了0N是S蕴涵，R蕴涵和QL蕴涵的等价条件，重点为QL蕴涵的等价条件；研究了一
2、个二元函数1成为的等价条件及蕴涵满足性质Hx,N(x))=N(x)和/(x,y)=/(x,/(x,y))的条件；同时讨论了算子T「n是t-模的充分必要条件.最后，我们研究了蕴涵1"的推广S的性质，鉴于一般已不再是模糊蕴涵，我们给出了叭是模糊蕴涵的条件；讨论了叭算子对常见的模糊蕴涵性质的满足情况和证明了由表现统一模U生成的就是Ru蕴涵；最后我们讨论了算子S.n成为统一模的条件.关键词：模糊蕴涵，S蕴涵，R蕴涵，QL蕴涵，逆否对称性ASTUDYONAFAMILYOFFUZZYIMPLICATIONSABSTRACT
3、Inthispaper,westudythepropertiesofafamilyoffuzzyimplicationsIt.nanditsextensionIu.nindetail.Themainresearchworkissummarizedasfollows.Firstly,wepresentanoverviewofthecurrentstudyonfuzzyimplicationsanduninormswhichmainlyincludesthedetailedinvestigationintother
4、esearchonthepropertiesofthreefamiliesofusualimplications(S-implications,/^-implicationsand0Q-implications),fuzzyimplicationsandoperatorsgeneratedfromuninorms,andtheircharacterizations.Then,webrieflyintroducesomeconceptsoffuzzylogicconnectives(negations,t-nor
5、ms,t-conorms,fuzzyimplications).Secondly,westudythepropertiesofafamilyoffuzzyimplicationsIt.nindetail.WegivetheconditionsunderwhichIt.nisafuzzyimplicationandtheconditionsunderwhichIt9nisanS-implication,R-implicationorQL-implication(mainpart).Meanwhile,wealso
6、investigatetheconditionsunderwhichafunctionIisIt.nandtheconditionsunderwhichIt.nsatisfiesthepropertiesI(x.N(x))=N(x)and太凍理工大学硕士研究牛学位论文/(x,y)=/(x,/(%,y))•Inaddition,wediscussthenecessaryandsufficientconditionunderwhichTi.nisat-norm.Finally,westudythepropertie
7、sofanextensionIu.nofIt.n,InviewthatIu.nisnotafuzzyimplicationgenerally,wegivesomeconditionsunderwhichIu.nisfuzzyimplication,andtheconditionsunderwhichIu.nsatisfiesfuzzyimplicationsandprovethatsgeneratedfromrepresentableuninormUisanRu-implication.Atlast,wedis
8、cussthenecessaryandsufficientconditionunderwhichUi、nisauninorm.KEYWORDS:fuzzyimplication,S-implications,/^-implications,2^-implications,contrapositivesymmetryin主要符号说明任意L存在□屈于N模糊非Nc标准非ND2对偶直觉非T八模
