Introduction to fuzzy arithmetic: theory and applications.

*(English)*Zbl 0754.26012
New York etc.: Van Nostrand Reinhold. xvii, 361 p. (1991).

The book under review is the first one to present a comprehensive and self-contained theory of fuzzy numbers and its applications. The authors systematically sum up all the works about the fuzzy numbers in the past decades. What’s more, the authors also present many of the concepts and techniques that are original and appear in the literature for the first time. In particular, they mainly present the concept of hybrid numbers discussed in Chapter 3 (Fuzzy trigonometric functions and complex numbers) and a fuzzy generalization of the theory of catastrophes. Moreover, they have also introduced some new concepts. The authors’ exposition of these and other concepts and techniques is thorough and well organized and points to a wide variety of applications in systems analysis, decision making under uncertainty, and other fields. Readers must be greatly impressed by the wide variety of concepts and techniques that the authors discuss so well and with so many carefully worked-out examples.

Reviewer: Wang Peizhuang (Kent Ridge)