Fuzzy Set Theory: Foundations and Applications / Edition 1by George J. Klir, Ute St. Clair, Bo Yuan
Pub. Date: 04/17/1997
Publisher: Prentice Hall
This book is designed to help anyone understand the basics of fuzzy sets, whether or not they have a mathematical background. The book first presents a basic grounding in information theory, classical logic and set theories. Next, it introduces the basics of fuzzy sets, distinguishing them from traditional crisp sets, and introducing the concept of/b>/b>
This book is designed to help anyone understand the basics of fuzzy sets, whether or not they have a mathematical background. The book first presents a basic grounding in information theory, classical logic and set theories. Next, it introduces the basics of fuzzy sets, distinguishing them from traditional crisp sets, and introducing the concept of membership function. The distinctions between classical and fuzzy relations are introduced, as are representations of fuzzy relations; fuzzy equivalence relations; fuzzy partial orderings, and related topics. The book introduces fuzzy arithmetic and fuzzy numbers. It also presents a detailed introduction to fuzzy logic, multivalued logics, fuzzy propositions, quantifiers, linguistic hedges and approximate reasoning. Several basic and advanced applications for fuzzy set theory are presented as well. Any non-technical reader interested in fuzzy sets and fuzzy logic. Also ideal for introductory level-students, whether they are planning a technical or non-technical course of study.
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Table of Contents
Information, Uncertainty, and Complexity.
Measurement and Uncertainty. Language and Vagueness. The Emergence of Fuzzy Set Theory. Fuzzy Set Theory Versus Probability Theory.
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.
Introduction. Representations. Equivalence Relations. Partial Orderings. Projections and Cylindric Extensions.
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.
Introduction. Multivalued Logics. Fuzzy Propositions. Fuzzy Quantifiers. Linguistic Hedges. Approximate Reasoning.
Applications: A Survey.
An Historical Overview.
References for Applications.
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