The Construction Of Implication Operator In Fuzzy Logic

In this thesis,we investigated the construction of implication operators in fuzzy logic.The main contributions of this thesis are summarized as follows:In chapter 1,we briefly introduced the development of fuzzy logic and the present domestic and foreign research' s situation.Preparatory knowledge including some definitions and theorems were also given because we would use them next chapters.Besides,some definitions and properties of several kinds of common implication operators over[0,1]were introduced.In chapter 2,generalized normal forms in BL-algebra and their contribution to universal approximation of L—functions were reviewed.And the possibility was proved that some L—functions can be precisely represented by the respectively discrete conjunctive normal form.In chapter 3,this chapter continued the investigation of approximating properties of generalized normal forms in fuzzy logic.The ability of Perfect normal forms and other normal forms in MV-algebra of FL-functions for approximate representation of uniformly continuous functions were investigated.In chapter 4,we proved that(?)x⊕y,(?)m·x⊕n·y,(?)x⊕n·y, (?)m·x⊕y are strong implication operators in Lukasiewicz System.Then we showed the result that the conjunction and disjunction of some arbitrary Lukasiewicz strong implication operators are strong implication Operators.In the last part,some viewpoints about the problem of constructing strong implication operators in Lukasiewicz System are presented.In chapter 5,the final chapter summarized this paper' s research work and several questions expected to solve.