HEDGE ALGEBRAS, LINGUISTIC-VALUE LOGIC AND THEIR APPLICATION TO FUZZY REASONING

Abstract

People use natural languages to think, to reason, to deduce conclusions, and to make decisions. Fuzzy set theory introduced by L. A. Zadeh has been intensively developed and founded a computational foundation for modeling human reasoning processs. The contribution of this theory both in the theoretical and the applied aspects is well recognized. However, the traditional fuzzy set theory cannot handle linguistic terms directly. In our approach, we have constructed algebraic structures to model linguistic domains, and developed a method of linguistic reasoning, which directly manipulates linguistic terms, In particular, our approach can be applied to fuzzy control problems. In many applications of expert systems or fuzzy control, there exist numerous fuzzy reasoning methods. Intuitively, the effectiveness of each method depends on how well this method satisfies the following criterion: the similarity degree between the conclusion (the output) of the method and the consequence of an if-then sentence (in the given fuzzy model) should be the "same" as that between the input of the method and the antecedent of this if-then sentence. To formalize this idea, we introduce a "measure function" to measure the similarity between linguistic terms in a domain of any linguistic variable and to build approximate reasoning methods. The resulting comparison between our method and some other methods shows that our method is simple and more effective.