Fuzzy Set Theory — and Its Applications

Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances have been made in many directions. In fact it seems extremely difficult for a newcomer to the field or for somebody who wants to apply fuzzy set theory to his problems to recognize properly the present "state of the art." Therefore, many applications use fuzzy set theory on a much more elementary level than appropriate and necessary. On the other hand, theoretical publications are already so specialized and assume such a background in fuzzy set theory that they are hard to understand. The more than 4,000 publications that exist in the field are widely scattered over many areas and in many journals. Existing books are edited volumes containing specialized contributions or monographs that only focus on specific areas of fuzzy sets, such as pattern recognition [Bezdek 1981], switching functions [Kandel, Lee 1979], or decision making [Kickert 1978]. Even the excellent survey book by Dubois and Prade [1980] is primarily intended as a research compendium for insiders rather than an introduction to fuzzy set theory or a textbook. This lack of a compre- hensive and modern text is particularly recognized by newcomers to the field and by those who want to teach fuzzy set theory and its applications.