Overview

Providing the background for understanding fuzzy set theory, even for non-mathematicians, this manual presents a basic background in information theory, classical logic and set theories. It then introduces the basics of fuzzy sets, and the concept of membership function. The distinctions between classical and fuzzy relations are shown, as are representations of fuzzy relations, fuzzy equivalence relations, fuzzy partial orderings and related topics. The book also introduces fuzzy arithmetic and fuzzy numbers, and a detailed introduction to fuzzy logic, multivalued logics, fuzzy propositions, quantifiers, linguistic hedges and approximate reasoning. Several basic and advanced applications for fuzzyu set theory are also presented.

Full Product Details

Author:   George J. Klir ,  Ute St. Clair ,  Bo Yuan
Publisher:   Pearson Education (US)
Imprint:   Prentice Hall
Edition:   US ed
Dimensions:   Width: 23.50cm , Height: 1.50cm , Length: 15.50cm
Weight:   0.336kg
ISBN:  

9780133410587

ISBN 10:   0133410587
Pages:   256
Publication Date:   22 May 1997
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

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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