The primary purpose of this book is to present information about selected topics on the interactions and applications of fuzzy + neural. Most of the discussion centers around our own research in these areas. Fuzzy + neural can mean many things: (1) approximations between fuzzy systems and neu� ral nets (Chapter 4); (2) building hybrid neural nets to equal fuzzy systems (Chapter 5); (3) using neura.l nets to solve fuzzy problems (Chapter 6); (4) approximations between fuzzy neural nets and other fuzzy systems (Chap� ter 8); (5) constructing hybrid fuzzy neural nets for certain fuzzy systems (Chapters 9, 10); or (6) computing with words (Chapter 11). This book is not intend to be used primarily as a text book for a course in fuzzy + neural because we have not included problems at the end of each chapter, we have omitted most proofs (given in the references), and we have given very few references. We wanted to keep the mathematical prerequisites to a minimum so all longer, involved, proofs were omitted. Elementary dif� ferential calculus is the only prerequisite needed since we do mention partial derivatives once or twice.

From the Back Cover

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.

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