Fuzzy Principle Algorithm based on Mathematical Theory

Abstract

Fuzzy reasoning algorithm is the key content in fuzzy logic research, and is also the basic theory in fuzzy control. With the deepening of the research, currently a lot of fuzzy reasoning algorithms are proposed and applied in electrical appliances and many industrial productions. But its basic research and theory are relatively weak. This paper studies fuzzy reasoning algorithm based on the principle of mathematics and verifies three theorems. The results show that there is a bounded real function between the conclusion and premise of a variety of fuzzy reasoning algorithms, and different algorithms are the transformation in structure form of the function. This verifies the reliability of fuzzy reasoning algorithm. Professor L.A.Zadeh at the University of California in 1965 first put forward the basic theory and thought of fuzzy mathematics, which laid the foundation of fuzzy mathematics. In 1973, it was first applied in control. Zaheh developed the way to apply fuzzy reasoning on the basis of fuzzy mathematics and it played an important role in analyzing and solving the problems of FMP and FMT. This method was applied in fuzzy control afterwards. The widely application of fuzzy reasoning also makes it the important position in fuzzy system theory study. Currently, the most widely used method in industrial production is still CRI method proposed by professor Zadeh, but this method has some problems which also lead people to urgently seek for better reasoning algorithms. For decades, CRI method is expanded and constantly fused into more new compound operation methods and fuzzy definition relations, and a variety of fuzzy reasoning methods are obtained. In addition to basic CRI method, there are analogical reasoning algorithm based on similarity degree, interval-valued reasoning methods, and evidence reasoning method. J.F.Baldwin highlights logic characteristics of approximate reasoning, and puts forward a method based on true value limit. There are also a lot of research at home, for example, professor Wang Guojun put forward a kind of brand-new full implication triple I algorithm in 1999 in our country on the basis of in-depth study of CRI algorithm. In addition to further correction of CRI, it also innovatively puts forward the research direction of logical semantic implication. I. CLASSICAL ALGORITHM STUDY OF FUZZY REASONING A. FMP model and CRI algorithm FMP, namely fuzzy modus ponens, is the basic model for fuzzy reasoning algorithm and the basic format is expressed as: Hypothesis I: if x is A, then y is B, Hypothesis II: if x is A ', conclusion y is B', and the formal representation is as follows: