FUZZY SETS AND FUZZY LOGIC Theory and Applications GEORGE J. KLIR AND BO YUAN Forbook and bookstore Intomtat/on http Jtwww.prenhall.com gopher to gopher.pranhall.com -- Prentice Hall P T R Upper Saddle River, New Jersey 07458 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 The publisher offers discounts on this book when ordered in bulk quantities. For more information, contact: Corporate Sales Department Prentice Hall PTR One Lake Street Upper Saddle River, NJ 07458 Phone: 800-382-3419 Fax: 201-236-7141 e-mail:
[email protected] All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN 0-13-101171-5 Prentice-Hall International (UK) Limited, London Prentice-Hall of Australia Pty. Limited, Sydney Prentice-Hall of Canada Inc., Toronto Prentice-Hall Hispanoamericana, S.A., Mexico Prentice-Hall of India Private Limited, New Delhi Prentice-Hall of Japan, Inc., Tokyo Simon & Schuster Asia Pte. Ltd., Singapore Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro 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