Research On Fuzzy Reasoning Methods And Fuzzy Logic Formal Systems

The theory of fuzzy reasoning has made a great development, and got good results in application since the concept of fuzzy sets was first introduced by Zadeh in 1965. Up to now, there exist a lot of fuzzy reasoning methods. Those methods made successful improvement in various research fields of theory and application, but took little effect on providing more reasonable logic foundation for fuzzy reasoning. This problem is due in part to there is no any universal criterion to judge all those fuzzy reasoning methods good or not. Otherwize, a universal criterion cannot be expected overnight because of the diversity and complexity of fuzzy reasoning, it requires a long-time research.There are many important properties of fuzzy reasoning methods, among them, the property of being consistent is most important and has been most noticed. Now, consistency is the most important one criterion of fuzzy reasoning methods accepted by most people. Formerly although many scholars have studied the property of being consistent, they have regarded the property as one kind of fuzzy reasoning and lack of essentially conducted the contrast research. So as the most important one criterion of fuzzy reasoning methods, it is necessary to study the consistency of fuzzy reasoning methods from every side. Furthermore, improve the existing fuzzy reasoning methods, or propose a new excellent fuzzy reasoning method, base on a comprehensive summary of the existing research.h outcomes. Those outcomes can provide a basis for a universal criterion. Otherwize, reasoning is inseparable from logic. The reasoning capacities of formal logic systems also play a major role in fuzzy theory. It is necessary to study depthly on fuzzy logic formal systems while studing on fuzzy reasoning methods.In this paper, the properties of being consistent of the existing fuzzy reasoning methods are essentially contrast researched, especially the four methods:Zadeh's CRI method, Wang's Triple I Method, Truth-Valued flow method and Turksen et al.'s AARS method, then a conclusion that the consistency of a fuzzy reasoning method is correlative with its reasoning mechanism is introduced, and a consistent based on similarity measure with thresholds is proposed based on the conclusion. Detailedly, first the major computations between fuzzy sets and implication operators are introduced, and the kinds of fuzzy reasoning forms are summarized. Then the definitions of the consistency of GMP and GMT with thresholds are proposed, and some examples are given to show that the existing fuzzy reasoning methods are almost not consistent for multiple rules. Consequently, a consistent fuzzy reasoning algorithm based on similarity measure with thresholds is proposed, which is proved to be consistent for multiple rules in this paper. Some results are given to show that the consistent fuzzy reasoning algorithm based on similarity measure with thresholds is workable. Finally, a fuzzy logic formal system and its dual formal system are established.In view of the problems about fuzzy logic and fuzzy reasoning, a thorough study are made on fuzzy reasoning methods and their logic foundations。The study results in this paper are expected to improve and perfect fuzzy theory to a certain degree, and lay a solid foundation in following research.