On Several Kinds Of Implications In Fuzzy Reasoning

Fuzzy reasoning is one of the most important branches of fuzzy mathematics. Fuzzy reasonings and fuzzy implication operators are closely related. Different implication operators will lead to different conclusions. Various fuzzy implication operators were proposed based on practical problems in the literature. The researches of implication operators are of significance in both respects of theory and application. This paper is devoted to the study of fuzzy implication operators and their applications in fuzzy reasoning. The paper mainly contains following three parts:1. The study of fuzzy Xor connectives and fuzzy Xor connective based implication operators.In order to investigate fuzzy reasoning deeply, it is necessary to constructive new implication operators. Some properties of fuzzy Xor connective are derived. Three kinds of implication operators are obtained by the composition of fuzzy Xor, t-norm, t-conorm and fuzzy negation. The relationships between the three implication operators and automorphisms are discussed. Some examples of RE,N,T are given.2. The study of fuzzy XNOR connectives and fuzzy XNOR connective based implication operators.The notion of fuzzy XNOR connective is presented, which is a generalization of the classical XNOR connective and preserves the main properties of the classical XNOR connective. Two kinds of implication operators based on the composition of fuzzy XNOR, t-norm, t-conorm and fuzzy negation are provided. Their relationships with automorphisms are analyzed.3. TripleⅠmethod of interval-valued fuzzy reasoning based on S-implication.S-implications are used extensively in fuzzy logic. TripleⅠmethod is a new kind of fuzzy reasoning with respect to FMP and FMT. In this part, some properties of S-implications are derived. The [α,β]-tripleⅠFMP principle and [α,β]-tripleⅠFMT principle are given. The reasoning methods with reapect to [α,β]-tripleⅠFMP and [α,β]-tripleⅠFMT are presented. Additionally, the reversibility properties of tripleⅠmethods are also discussed.