Hedge algebras, linguistic-valued logic and their application to fuzzy reasoning

People use natural languages to think, to reason, to deduce conclusions, an d to make decisions. Fuzzy set theory introduced by L. A. Zadeh has been in tensively developed and founded a computational foundation for modeling hum an reasoning processes. The contribution of this theory both in the theoret ical and the applied aspects is well recognized. However, the traditional f uzzy set theory cannot handle linguistic terms directly. In our approach, w e have constructed algebraic structures to model linguistic domains, and de veloped a method of linguistic reasoning, which directly manipulates lingui stic terms. In particular, our approach can be applied to fuzzy control pro blems. In many applications of expert systems or fuzzy control, there exist numero us fuzzy reasoning methods. Intuitively, the effectiveness of each method d epends on how well this method satisfies the following criterion: the simil arity degree between the conclusion (the output) of the method and the cons equence of an if-then sentence (in the given fuzzy model) should be the "sa me" as that between the input of the method and the antecedent of this if-t hen sentence. To formalize this idea, we introduce a "measure function" to measure the similarity between linguistic terms in a domain of any linguist ic variable and to build approximate reasoning methods. The resulting compa rison between our method and some other methods shows that our method is si mpler and more effective.