1 As a treatise on fuzzy set theory and its applications, Foundations of Fuzzy Systems, by R. Kruse, J. Gebhardt and F. Klawonn, has few equals. Succinct, authoritative and up-to-date, it covers the basic theory very thoroughly and precisely, with emphasis on those aspects of the theory which play an important role in its applications. This is especially true of the chapters dealing with the calculus of fuzzy if-then rules - a subset of fuzzy set theory which plays a central role in the applications relating to the conception and design of both control and knowledge-based systems. To view the contents of Foundations of Fuzzy Systems in a proper perspective, a digression is in order. First, it is important to recognize that any crisp theory X can be fuzzified and hence generalized to fuzzy X - by replacing the concept of a crisp set in X by that of a fuzzy set. In application to basic fields such as arithmetic, topology, graph theory.