The term “fuzzy sets” has been introduced to describe, in precise mathematical terms, the ambiguities and uncertainties inherent in many real-world pattern recognition and classification problems. The promotional material attached to this book claims that this is “ . . . the first complete presentation of fuzzy mathematics available.” However, the reviewer cannot help but notice that a significant part of the text, comprising some 50 pages out of 225 (not counting references), is lifted verbatim from the author’s earlier text [1]. More importantly, the old part contains all the basic ideas; the added material is comprehensive only in the sense of squeezing the last bit of juice out of them. This is done in a rather careless and superficial manner, leaving the reader wondering about the real content and significance of the material. The lack of a glossary for the many unconventional and generally ill-chosen notations adds to the confusion. Especially disappointing is the chapter on applications. Given the author’s background and the more than 40 pages of references, one would expect to find some worthwhile applications of fuzzy sets to significant real-world problems. Instead, only generalities are presented with some very contrived examples that nevertheless can be treated as well, if not better, by conventional methods.

For the reasons given, this book cannot be recommended for any purposes. The reader who wants to get some of the flavor of fuzzy set ideas is much better off with the author’s earlier book which contains, in addition to the basic mathematics, at least some concrete applications and which is much more carefully written. A good deal of the blame for the problems of this book has to go to the editorial staff of Addison-Wesley, who should never have allowed this text to go to print without major reworking.

The chapters of the book are as follows: (1) Fuzzy Sets; (2) Possibility Theory and Fuzzy Quantification; (3) Fuzzy Functions; (4) Fuzzy Events and Fuzzy Statistics; (5) Fuzzy Relations; (6) Fuzzy Logics; and (7) Some Applications. The book also features a Bibliography and an Index.