(I, A)-A Description Of Implication And Fuzzy Implication That Satisfies The MV Characteristic Equation

Fuzzy implications play a fundamental role in fuzzy logic and approximate rea-soning,and the construction of fuzzy implications is an important research topic in related fields.According to construction methods,fuzzy implications can be by roughly classified into five classes,namely,material implications,residual implica-tions,quantum implications,Yager implications and ordinal sum implications.On the other hand,the study of the algebraic properties of fuzzy implications is also one of the current hot topics.The characterizations for fuzzy implications to satisfy certain characteristic equations are the main research direction of their algebraic properties.This thesis studies the fuzzy implications from the above two aspects of structural and equational characterizations.Firstly,based on fuzzy implication and aggregation operator,the notion of(I,A)-implication is introduced,and some basic properties of(I,A)-implications are discussed,including distributivity and law of importation.Secondly,the complete characterizations of well known fuzzy impli-cations satisfying MV characteristic equation are given.The concrete content is as follows:Chapter One:Preliminaries.In this chapter,some basic concepts and rele-vant conclusions of aggregation operator,fuzzy negation and fuzzy implication are reviewed.Chapter Two:(I,A)-implieation and its properties.Firstly,(I,A)-operator is constructed based on fuzzy implication I and aggregation operator A,and basic properties of(I,A)-operator are investigated.Secondly,the sufficient conditions un-der which(O,A)-operators are fuzzy implications are discussed.Lastly,distributivity separately over overlap functions and grouping functions and law of importation of(I,A)-implications are given.Chapter Three:Characterizations of fuzzy implications satisfying MV char-acteristic equation.Firstly,the relations between MV characteristic equation and the properties of fuzzy implications are studied.Secondly,characterizations of(S,N)-implications,R-implications and QL-implications which are obtained from continuous t-norms satisfying MV characteristic equation are given.Lastly,the re-marks that f-,g-and h-implications don't satisfy MV characteristic equation are given.