The Formalization Theory Of Fuzzy Reasoning

The Formalization Theory of Fuzzy ReasoningYuan HejunAbstract Since L.A.Zadeh proposed the concept of fuzzy set in 1965, the study on fuzzy system has got rapid development. Fuzzy control has made enormous success in application, but its basic theory------fuzzy reasoning, still hasn't adependable logical base. In 1996, professor Wang Guojun built formal deductive system L* of fuzzy prepositional calculus, then in the frame of system L*, constructed the logical base for fuzfcy reasoning rules from sematics. Again in 1999, based on RQ implication operator prof.Wang proposed triple-I method of fuzzy reasoning, which is more reasonable than the CRI method that was proposed by Zadeh and now is widely applied in control field. The aim of this paper is to give a logical base for fuzzy reasoning rules from syntactic point of view and to study the non-fuzzy form of fuzzy reasoning.In the first part, as preparatory knowledge, this paper gives a general form of triple-I method of fuzzy reasoning, which is based on the residua-type implication operator. It provides a foundation for the later study of non-fuzzy form of fuzzy reasoning.The second part builds a new algebra syetem RL, which in the definition of BL-algebra gets rid of the stronger condition and studies the properties of RL-algebra. In the same time, Using RL-algebra as the true-value field this paper builds a more extentively formal deductive system of fuzzyprepositional calculus------logic system RL. obtains a series of theorems, and studiesthe completeness of RL logic.The third and the fourth part of this paper is studying the root theory of fuzzy logic and the formalization theory of fuzzy reasoning from the syntactic view. The conclusion is obtained that in fuzzy logic systems there exists the completely similar reasoning mechanism to fuzzy reasoning.The fifth part is studying the formalization theory of fuzzy reasoning from the semantic angle, and obtains the non-fuzzy form of the triple-I FMP solve and triple-I FMT solve of fuzzy reasoning.In the last, the problem of the perturbation of fuzzy reasoning is discussed in detail, and the maximum perturbation parameters for various methods of fuzzy reasoning is estimated according to the choice of conjunctive operator and implication operator.