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Reviewer: Heinrich W. Guggenheimer

Klir and Yuan's book is both a textbook and a kind of encyclopedia of the current state of fuzzy set theory. It does not presuppose any knowledge of fuzzy sets, nor even of classical set theory. The book has two parts, one theoretical and one applied. The theoretical part is detailed and methodical, giving full explanations and motivations. The necessary background is explained in two introductory chapters. A third chapter introduces the basic operations on fuzzy sets in general, removed from crisp paradigms. The remainder of the theoretical part is devoted to fuzzy arithmetic, fuzzy relations, fuzzy equations, possibility theory, fuzzy logic, and uncertainty-based information. The treatment is thorough and almost complete. In applications, one rarely has to deal with more than one composition operator on fuzzy data at a time. The one subject missing in the theoretical part is the spread of fuzziness by repeated compositions; in most cases, the uncertainty expressed by the membership function spreads rapidly over the entire interval under consideration to make the results of questionable usefulness. Practical criteria on the loss of usefulness in more than two compositions would be useful. The second part, on applications, is by necessity more of a report, al though certain aspects of system theory and neural networks are treated in enough detail to introduce the novice to the subject. Here the superb bibliography of 1731 items, supported by a separate bibliographic index, becomes an integral part of the text and gives ample material for anyone interested in a specific type of application, from civil engineering to pattern recognition and decision making. All in all, I highly recommend this useful book to everyone involved in any engineering task involving uncertainty and error tolerances.