Triple Ⅰ Reasoning Method On Interval-Valued Fuzzy Sets

Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT ) are two kinds fuzzy reasoning models .It is one of the most important fields to investigate FMP and FMT reasoning models on the theory of fuzzy reasoning .Triple I method is a new kind fuzzy reasoning method with respect to FMP and FMT reasoning models. Interval-valued fuzzy reasoning is special reasoning method . Therefore it is given in this paper that triple I algorithm of fuzzy reasoning on interval-valued fuzzy sets is discussed, two parts are included as following . Part One On the Study of Interval Value and Interval-valued Fuzzy SetsIt is given that definitions of pseudo-order ,intersection ,union , complete ,implication and T -norm on interval value and interval- valued fuzzy sets, their properties are discussed respectively. It is the foundation on studying interval valued fuzzy reasoning. Part Two Triple I Method On Interval-valued Fuzzy SetsFirst of all, it is investigated that triple I algorithm on Zadeh fuzzy sets under a general implication operator. Secondly, it is also investigated that triple I algorithm on interval-valued fuzzy sets under two kinds different implication operators, [a,B]-triple I FMP principle and [a,B]- triple I FMT principle are given ,an algorithm which can be obtained the solution of[a,B]-triple I FMP and [a,B]-triple I FMT is given . It is also discussed that the solutions of triple I FMP and triple I FMT are reductive respectively on some special conditions. Finally opposite direction triple I method under Lukasiewicz implication operator on Zadeh fuzzy sets is discussed .