This book is about recent research area described as the intersection of fuzzy sets, (layered, feedforward) neural nets and evolutionary algorithms. Also called "soft computing". The treatment is elementary in that all "proofs" have been relegated to the references and the only mathematical prerequisite is elementary differential calculus. No previous knowledge of neural nets nor fuzzy sets is needed. Most of the discussion centers around the authors' own research in this area over the last ten years. The book brings together results on: (1) approximations between neural nets and fuzzy systems; (2) building hybrid neural nets for fuzzy systems; (3) approximations between fuzzy neural nets for fuzzy systems. New results include the use of evolutionary algorithms to train fuzzy neural nets and the introduction of a "fuzzy teaching machine". The interaction between fuzzy and neural is also illustrated in the use of neural nets to solve fuzzy problems and the use of fuzzy neural nets to solve the "overfitting" problem of regular neural nets. Besides giving a comprehensive theoretical survey of these results the authors also survey the unsolved problems in this exciting, new, area of research.