Research For Improved The Full Implication Reasoning Method And Its Properties

In 1999,Professor Wang Guojun,a famous Chinese mathematician,proposed the full implication reasoning method(three I method for short)in fuzzy reasoning,which effectively improved the traditional fuzzy reasoning method,i.e.CRI method.In the past ten years,extending and improving the three I method,has become one of the most hot research direction of fuzzy logic and fuzzy reasoning.This paper focuses on the improvement of the three I method,and proposes two new methods of fuzzy reasoning,and discusses their properties respectively.In recent literatures,the five I reasoning method based on the three I method has been proposed,which made a significant improvement to the three I method.We observe that the five implications in the five I method all are taken the same implication.However,this may lead to some difficulties to applied fields such as fuzzy control.Therefore,this paper improves this reasoning method and proposes an improved five I reasoning method,called the general full implication reasoning method.Then for two basic inference models FMP and FMT,the unified algorithm expressions of the new method are given,and the reductivity and robustness of the new inference algorithms are discussed.Fuzzy similarity is a kind of measure degree of similarity between fuzzy sets.On the basis of the general full implication reasoning method,this paper combines fuzzy similarity to propose a general full implication reasoning method,and gives the unified algorithms for FMP and FMT,and discusses reductivity of these two algorithms respectively.In view of the important position of fuzzy implication in fuzzy reasoning,the construction of fuzzy implications and their properties have been one of the important research topics in fuzzy logic.On the other hand,Copulas generated from probability theory and statistics are a kind of special aggregation functions.This kind of aggregation functions have important applications in finance,decision analysis and fuzzy logic.In particular,Copulas can also generate fuzzy implications.The fuzzy implications generated by Copulas are further explored in this paper,and a novel method of generating fuzzy co-implication by Copulas and fuzzy negations is proposed.Combined with fuzzy negation,fuzzy co-implications are transformed into fuzzy implications.Moreover,we generate a fuzzy implication family based on an important Copula family and apply them to fuzzy reasoning.