I can't say that anything has been "exciting". Rather, I would choose the word "interesting". Not too long ago, the Chinese University of Hong Kong conducted a survey to determine which consumer products were using Fuzzy Logic. The result was a thick report, some 150-200 pages long-washing machines, camcorders, microwave ovens, etc. What interested me wasn't the particular applications so much as the breadth of applications-so many products were incorporating Fuzzy Logic.

A frequent source of misunderstanding has to do with the interpretation of fuzzy logic. The problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FL<sub>n</sub>, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FL<sub>w</sub> is almost synonymous with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FL<sub>w</sub> is much broader than FL<sub>n</sub> and subsumes FL<sub>n</sub> as one of its branches; (b) the agenda of FL<sub>n</sub> is very different from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FL<sub>w</sub>

A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.