Fuzzy reasoning: an alternative to approximate reasoning theory

Applications of fuzzy logic to fuzzy control are very popular. However, for more general fuzzy reasoning problems, there are a number of important ideas that must be addressed. We discuss these topics: (1) The theory of approximate reasoning may be of dubious utility in fuzzy reasoning systems: we present examples of fuzzy rules which cannot be evaluated by approximate reasoning. (2) In fuzzy reasoning, it is intuitive that defuzzification be the inverse of fuzzification. (3) In some situations, the excluded middle law should be obeyed; this can be easily accomplished by switching to the Lukasiewicz logic when ANDing or ORing incompatible conditions. (4) Prior knowledge of confidences in data and of grades of membership of discrete fuzzy sets must be taken into account if multi-step reasoning is to be carried out. (5) A general-purpose fuzzy reasoning system should be a generalization of a non-fuzzy artificial intelligence based reasoning system, and should be able to do what nonfuzzy reasoning systems can do.