C.V. Negoita,Editors, ,Fuzzy Systems (1981) Abacus Press,New York 111

Book

reviews

217

This book is intended for readers of diverse backgrounds and intentionally involves some repetitions of ideas. It is an excellent discussion initiator and the author does a commendable job of presenting his theory. He claims that the theory is being used widely in corporate planning, and on an international scale in determining priorities of countries regarding their transport, industrial and agricultural infrastructure as well as to prioritize their natural resources for investment. Abraham Kandel Florida State University Tallahassee, FL. 32306 USA

Fuzzy Systems C.V. Negoita Abacus Press, Tunbridge

Wells, U.K.,

1981 (111 pp., f 16)

There is a great need for books designated primarily for the large audience. This is such a book. Fuzzy systems is a new discipline, both in the questions it asks and the method it uses to seek answers. So many alternative definitions of it have been proposed that the author preferred to avoid any attempt to define the discipline in a single sentence or paragraph. Instead, in this book he introduces the reader to fuzzy systems by letting the subject matter speak for itself. In 7 chapters (Introduction, An approach to complexity, Concepts decision and vagueness, Fuzzy sets, The categorical approach, Synthesis processes, Fuzziness in management) this book is intended to give some ideas of the type of problems that can be approached through the fuzzy set technology and the kinds of solutions that this technology suggests. By the time the reader finishes this book, he will have a better understanding of some of the pressing problems of the so-called soft sciences and some original insights into how solutions of these problems can be found. These are the real payoffs of studying fuzzy systems. There are also many hints for all those interested in fuzzy mathematics. It is known that Negoita has tried in the last five years to investigate the fundamentals. For instance, trying to extend the definition of a fuzzy set as a function f : X+ I,, where L is a lattice, to f : X --* JJ where R is classifier in a topos, he observed that neither the logic of Lukasiewicz nor the intuitionistic logic can be suggested as underlying the real logic of fuzzy sets. This is an important result which can lead to further developments in what we call fuzzy mathematics. More details about this topic can be found in the papers published later by the author in Fuzzy Sets and Systems and Bucefal, and not mentioned inthe 117 item bibliography of the book. This book reflects mainly the author’s view that fuzzy set technology is a body of thought with clear applications, a practical tool that can be used to explain natural phenomena.

218

Book reviews

The text deals with broad issues that confront human systems. The author emphasizes the usefulness of fuzzy systems theory to help social scientists meet the needs of modelling human systems in the way of using modern algebra to understand conflict resolution. Using the concept of ‘pullback’ from the theory of categories he suggests an interesting new view from structural stability. The presentation is clear and easy to read. The author presents his ideas in a convincing style with a fine touch when it comes to discussion of philosophical problems. This makes the reading especially enjoyable. Another point to be made is that the question that is answered here is answered originally. Not only is the temper detached and judicious, the facts well gathered and competently marshalled, but the expression of results is new. Apart from one or two concessions to the jargon of modern algebra, the author displays a verbal elegance. This text is beautiful and I recommend it to all those interested to see why fuzzy set technology has been born and is growing. Dan Ralescu University of Cincinnati Cincinnati, OH 45221 USA