Fuzzy logic—a personal perspective
This paper marks the 50th anniversary of the publication of my first paper on Fuzzy sets, Information and Control, 1965. What is of historical interest is that initially-and for some time thereafter-my paper was an object of indifference, skepticism and derision. A prominent school of thought claimed that set theory is probability theory in disguise. Positive comments were few and far between. In contrast, my ideas were welcomed with open arms in Japan. In the seventies and eighties of last century, set theory and logic began to gain acceptance in Europe and, more particularly, in Eastern Europe and the Soviet Union. In part, many negative reactions to my papers reflected the fact that the word fuzzy has pejorative connotations. In large measure, science is based on the classical, Aristotelian, bivalent logic. Binarization-drawing a sharply defined boundary between two classes-is a deeply entrenched Cartesian tradition. What is not widely recognized is that this tradition has outlived its usefulness. One of the principal contributions of logic is providing a basis for a progression from binarization to graduation, from binarism to pluralism, from black and white to shades of gray. Graduation involves association of a class which has unsharp (fuzzy) boundaries with degrees/grades of membership. Classes with unsharp boundaries are pervasive in human cognition. Most words in natural language are labels of such classes. This paper is a concise exposition of what I consider to be my principal contributions to the development of set theory and logic. Among the contributions which are discussed are: introduction of the concept of a set, FL-generalization, the concept of a linguistic variable, information granulation, precisiation of meaning, generalized theory of uncertainty (GTU), the concept of a restriction, restriction-centered theory of truth and meaning, the information principle, and similarity-based definitions of possibility and probability.