George J. Klir, T.J. Watson School Engineer & Applied Science, NY
Ute St. Clair, T.J. Watson School Engineer & Applied Science, NY
Bo Yuan, Las Vegas, New Mexico

Published April, 1997 by Prentice Hall PTR (ECS Professional)

Copyright 1997, 256 pp.
Cloth
ISBN 0-13-341058-7

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Preface.
Introduction.
Information, Uncertainty, and Complexity.

Measurement and Uncertainty. Language and Vagueness. The Emergence of Fuzzy Set Theory. Fuzzy Set Theory Versus Probability Theory.

Classical Logic.

Introduction. Propositional Logic. Predicate Logic. Classical Set Theory.

Basic Concepts and Notation.

Set Operations. Fundamental Properties. Characteristic Functions of Crisp Sets. Other Concepts.

Fuzzy Sets: Basic Concepts and Properties.

Restrictions of Classical Set Theory and Logic. Membership Functions. Representations of Membership Functions. Constructing Fuzzy Sets. Operations on Fuzzy Sets.

Fuzzy Sets: Further Properties.

a-Cuts of Fuzzy Sets. a-Cut Representation. Cutworthy Properties of Fuzzy Sets. Extension Principle. Measurement of Fuzziness.

Classical Relations.

Introduction. Representations. Equivalence Relations. Partial Orderings. Projections and Cylindric Extensions.

Fuzzy Relations.

Introduction. Representations. Operations on Binary Fuzzy Relations. Fuzzy Equivalence Relations and Compatibility Relations. Fuzzy Partial Orderings. Projections and Cylindric Extensions. Fuzzy Arithmetic. Fuzzy Numbers. Arithmetic Operations on Intervals. Arithmetic Operations on Fuzzy Numbers.

Fuzzy Logic.

Introduction. Multivalued Logics. Fuzzy Propositions. Fuzzy Quantifiers. Linguistic Hedges. Approximate Reasoning.

Applications: A Survey.
An Historical Overview.
Established Applications.
Prospective Applications.
Illustrative Examples.
References for Applications.

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