Fuzzy Sets and Fuzzy Logic
Quite a long time after its inception in about 1965, the field of fuzzy sets and fuzzy logic was ranked to be some exotic field of research. The main rea son was its seeming tendency away from "hard" mathematical modelling and thus - as often supposed by mathematically inclined outsiders - completely away from an acceptable mathematically based theory. The very recent success with even consumer products involving fuzzy tools causes a rapidly growing interest of the engineering community in this field. But it may also become responsible for a far more extended interest from mathematicians and computer scientists. The term "fuzzy logic" has undergone an almost continuous change. First it merely referred to tools from many-valued logic appearing in considera tions of fuzzy sets and sometimes of a generalized switching theory. Later it referred to the field of fuzzy logic control with its limited use of nonstandard reasoning by interpreting implication-like formulations of the rule oriented IF ••• THEN - type as fuzzy relations between the values of fuzzy variables. And the presently prevailing understanding is that of a theory of approxi mate reasoning (sometimes including the pure theory of fuzzy sets too).