Fuzzy Set Theory--and its applications, 3rd Ed.

International Journal of Electrical Engineering Education, Jul 1998 by Wolkenhauer, Olaf

Fuzzy Set Theory - and its applications, 3rd Ed.: H.-J. ZIMMERMANN (Kluwer Academic Publishers, 1996, 435 pp., 63.95, US$89.95) Professor Zimmermann describes fuzzy-set-theory as a

`very powerful modeling language that can cope with a large fraction of uncertainties in real-life situations. Because of its generality, it can be well adapted to different circumstances and contexts. In many cases, however, this will mean the context-dependent modification and specification of the original concepts of the formal fuzzy set theory. Regrettably, this adoption has not yet progressed to a satisfactory level, leaving an abundance of challenges....'

For the third edition of this book many new references have been added and chapters that referred to software tools are completely rewritten. The book presents an up-to-date, comprehensive and readable treatise on fuzzy-settheory and its applications. It is intended for students, lecturers and researchers in engineering and computer science.

The book is split into two parts: fuzzy mathematics and applications of fuzzy set theory. The first part covers basic definitions for fuzzy sets, the extension principle, fuzzy measures, fuzzy relations, fuzzy graphs, fuzzy analysis and possibility theory. The second part describes fuzzy logic in approximate reasoning applied to expert systems, fuzzy control and data analysis. Even though the book covers a large area of application, more emphasis is laid on expert systems for decision support. Professor Zimmermann himself applies fuzzy-set-theory to decision support systems in management and financial services. Therefore one finds an extensive description of models in operations research and decision making in the second part of the book (chapters 14, 15 and 16). Fuzzy control is dealt with in 37 pages. No specific approaches are introduced but a general description of a fuzzy controller structure is given and applications are illustrated. The chapters on approximate reasoning, fuzzy control and fuzzy data analysis include a brief description of available software and hardware tools. The carefully organised subject index makes the material very handy and easily accessible.

In my view, still the best comprehensive treatise of fuzzy-set-theory is given by Dubois and Prade (published by Academic Press). However, the book dates back to 1980 and is therefore not up-to-date. It is also not suitable as a course book, leaving the more recent book from Kruse, Gebhardt and Klawonn (published by Wiley) as one of the few alternatives to the book by Zimmermann. Kruse's book, even though it contains an excellent treatise on possibility theory and fuzzy control, does not cover as many research areas and applications as Zimmermann's book does.

Its suitability as a textbook is underlined by exercises at the end of each chapter. Professor Zimmermann has found a good balance of theory and practical applications giving an excellent introduction to fuzzy set theory. A teachers manual is available. Finally I would like to comment that, in my opinion, any book that is intended to serve as a course book should not cost more than 30 pounds....

OLAF WOLKENHAUER Control Systems Centre, UMIST