Fuzzy logic

Due to highly successful practical applications, developed primarily in Japan, fuzzy logic is receiving considerable attention. In this context, “fuzzy logic” is broadly viewed as a system for dealing with reasoning that is approximate rather than exact. In the narrow sense, the term refers to a generalization of the various many-valued logics. This narrow sense of fuzzy logic is not of interest here. Fuzzy sets, upon which fuzzy logic is based, and some basic ideas pertaining to their theory were first introduced in 1965 by Lotfi A. Zadeh. The reaction to his rather radical proposal was mixed. A few scholars greeted it with enthusiasm, but many expressed skepticism, and some were even openly hostile. Three rather natural phases in the development of fuzzy set theory and the derivative fuzzy logic followed. (1) The “academic phase” (1965-77) characterized by the development of the basic ideas of fuzzy set theory and some initial speculations about its prospective applications. The outcome was a rather small number of publications by a small number of contributors, primarily from the academic community. (2) The “transformation phase” (1978-1988) characterized by significant advances in theory and some initial evidence of successful practical applications