The Theory Of Fuzzy Logic Based On Family Of Implication Operators

Recently, fuzzy control has achieved remarkable success in application. However, as the core of fuzzy control, fuzzy reasoning is short of strict mathematical foundation. Therefore, modern fuzzy logic mainly study the mathematical basis of fuzzy reasoning, as a new field of mathematics, it has attracted the attention of many scholars in the world and made a series of important research results. Moreover, fuzzy logic has a very wide range of applications. On the one hand, it has enriched and developed the research of pure mathematical theory. On the other hand, it has a wide range of applications in the areas of the approximate reasoning and fuzzy control.Implication operator with a parameter (i.e. the family of implication operators) is widely used in fuzzy control to design fuzzy controller. It has a certain degree of rationality for improving the control efficiency of fuzzy control. Therefore, the theme of this paper is to study the fuzzy logic theory of the family of implication operators and provide a new way for the applications of fuzzy reasoning in fuzzy control.The major research work and results are as follows:1. Study the basic properties of the family of fuzzy implication operators. We get the appropriate family of implication operators by some important t-norms. Then whether these families meet the sixteen conditions are investigated, and further the relationships of these families with a few important implication operator families are discussed.2. The theoretical research on generalized tautologies. Because the RDP logical system is important in fuzzy logic, in which the family of implication operators R p are used. Therefore, we choose the family of implication operators R p as the objects of our study, and analyse the theory of generalized tautology based on the fuzzy logic system that established by the family of implication operators. The results show that the system only has three different classes of generalized tautologies. In addition, the well-known upgrade algorithm used in many multi-valued logic systems and fuzzy logic systems are also used in the system. Our conclusions show that generally speaking, tautologies can not be derived from non-tautologies by repeatedly applying the upgrade algorithm finite times.3. Study tripe I method in fuzzy reasoning. We discussed the full implication inference based on the family of implication operators R p, the solutions for FMP and FMT based on tripe I andα-tripe I method are obtained respectively, which will help us to improve the flexibility and reduce the blindness of fuzzy reasoning.4. Study properties of fuzzy reasoning algorithms. We discussed the uniform continuity of the tripe I method in fuzzy reasoning, and obtained that triple I method in fuzzy reasoning by using the implication operators studied in this paper are uniformly continuous. The results show the superiority of the algorithm in a certain extent.5. Simulation. The tripe I method in fuzzy reasoning is applied to fuzzy control, and fuzzy controller is designed to guide practice. The results obtained by simulation experiments show that when the parameter takes different values, the control indexes are not the same. Thus, we can select the appropriate parameters to optimize the results of fuzzy control in the inference process.