Fuzzy systems handle imprecise concepts. Using fuzzy sets and fuzzy logic, one can build expert systems and controllers that have the advantages of being easy to understand, and of requiring less processing power than comparable neural net applications. The author lectures on fuzzy theory, and his book has the flavor of lecture notes. It is easy to read, very suitable for self-study or an introductory course, and has no embedded references in the text.

The first eight chapters develop fuzzy theory, while the last four briefly introduce applications. Each chapter ends with a summary and an exercise set. The exercises are mostly computational, to check one’s understanding of the material, but a few are proofs.

Chapter 1 defines a fuzzy set, in which a membership function assigns a number from 0 to 1 to every element of the universal set. A zero value indicates that the element is definitely not a member, while a value of one indicates that it definitely is. The values in between represent the fuzzy cases. The next five chapters cover fuzzy set operations, fuzzy relations, fuzzy graphs, fuzzy numbers, and fuzzy functions. Chapter 7 compares fuzzy theory with probability. The final theory chapter covers fuzzy logic.

Chapter 9, the first of the application chapters, presents fuzzy inference, discussing four different inference methods. This chapter provides a good foundation for the remaining ones, which cover fuzzy control and fuzzy expert systems, the fusion of fuzzy systems and neural networks, and the fusion of fuzzy system and genetic algorithms. These later chapters are brief introductions, encompassing only 70 pages.

Chapter 7 has three obvious misspellings in the first three pages. Other chapters have occasional errors in grammar. The book would have benefited from more proofreading.

The bibliography has 155 references, but it would have been much more helpful to include annotations, group them into categories, and refer to them at appropriate points within the text. Overall, this text is a pleasant way to approach an interesting subject.