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Introduction to

Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems

Introduction to

Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems
Guanrong Chen
University of Houston Houston, Texas

Trung Tat Pham
University of Houston, Clear Lake Houston, Texas

CRC Press Boca Raton London New York Washington, D.C.

Library of Congress Cataloging-in-Publication Data
Chen, G.(Guanrong) Introduction to fuzzy sets, fuzzy logic, and fuzzy control systems / Guanrong Chen, Trung Tat Pham. p. cm. Includes bibliographical references and index. ISBN 0-8493-1658-8 (alk. paper) 1. Soft computing. 2. Fuzzy systems. I. Pham, Trung Tat. II. Title. QA76.9.S63 C48 2000 0063—dc21


This book contains information obtained from authentic and highly regarded sources. Reprintedmaterial is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by anymeans, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC forsuch copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.

© 2001 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-1658-8Library of Congress Card Number 00-045431 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper

This textbook is an enlarged and enhanced version of the authors’ lecture notes used for a graduate course in fuzzy sets, fuzzy logic, fuzzy systems, and fuzzy control theories. This course has been taught for seven years at the University of Houston, withemphasis on fuzzy systems and fuzzy control, regarding both basic mathematical theories and their potential engineering applications. The word “fuzzy” is perhaps no longer fuzzy to many engineers today. Introduced in the earlier 1970s, fuzzy systems and fuzzy control theories as an emerging technology targeting industrial applications have added a promising new dimension to the existing domain ofconventional control systems engineering. It is now a common belief that when a complex physical system does not provide a set of differential or difference equations as a precise or reasonably accurate mathematical model, particularly when the system description requires certain human experience in linguistic terms, fuzzy systems and fuzzy control theories have some salient features anddistinguishing merits over many other approaches. Fuzzy control methods and algorithms, including many specialized software and hardware available on the market today, may be classified as one type of intelligent control. This is because fuzzy systems modeling, analysis, and control incorporate a certain amount of human knowledge into its components (fuzzy sets, fuzzy logic, and fuzzy rule base). Using humanexpertise in system modeling and controller design is not only advantageous but often necessary. Classical controller design has already incorporated human skills and knowledge: for instance, what type of controller to use and how to determine the controller structure and parameters largely depend on the decision and preference of the designer, especially when multiple choices are possible. The...
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