FUZZY SETS AND FUZZY LOGIC
Theory and Applications
GEORGE J. KLIR AND BO YUAN
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Library of Congress Cataloging-in-Publication Data Klir, George J., 1932Fuzzy sets and fuzzy logic: theory and applications / George J. Klir, Bo Yuan. p. cm. Includes bibliographical references and index.
ISBN 0-13-101171-5
1. Fuzzy sets. QA-248.K487
2. Fuzzy logic.
I. Yuan, Bo.
II. Title.
1995
511.3--dc20
94-36398
CIP
Editorial/production supervision: Patti Guerrieri Manufacturing buyer: Alexis R. Heydt Acquisitions editor: Paul Becker Editorial assistant: Maureen Diana Cover Design: Bo Yuan and Milena Klir Photographs: Milena Klir 01995 by George J. Klir Published by Prentice Hall PTR Prentice-Hall Inc. A Simon & Schuster Company Upper Saddle River, NJ 07458
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10 9 8 7 6 5 4 3 2 1 ISBN
0-13-101171-5
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To Lotfi Zadeh, Who had the courage and To begin thegrand paradigm shift, And to the many others, Whose hard work and healthy thinking Have contributed to the shifting.
CONTENTS
FOREWORD
PREFACE
xi xiii
PART I: THEORY
1
1. FROM CLASSICAL (CRISP) SETS TO FUZZY SETS: A Grand Paradigm Shift
1
1.1
1.2 1.3 1.4 1.5
Introduction Crisp Sets: An Overview Fuzzy Sets: Basic Types Fuzzy Sets: Basic Concepts Characteristics and Significance of the Paradigm Shift
Notes Exercises 2.
FUZZY SETS VERSUS CRISP SETS 2.1
2.2
2.3
3.
Additional Properties of a-Cuts Representations of Fuzzy Sets Extension Principle for Fuzzy