Fuzzy Systems Modeling and Control
The analysis and control of complex systems have been the main motivation for the emergence of fuzzy set theory since its inception. It is also a major research field where many applications, especially industrial ones, have made fuzzy logic famous. This
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THE KLUWER HANDBOOK SERIES ON FUZZY SETS Series Editors: Didier Dubois and Henri Prade
FUZZY SETS IN DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS, edited by Roman Slowmski ISBN: 0-7923-8112-2
FUZZY SYSTEMS Modeling and Control
edited by Hung T. Nguyen New Mexico State University
and
Michio Sugeno Tokyo Institute of Techno/ogy
111...
"
SPRINGER-SCIENCE+BUSINESS MEDIA, LLC
ISBN 978-1-4613-7515-9 ISBN 978-1-4615-5505-6 (eBook) DOI 10.1007/978-1-4615-5505-6
Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress.
Copyright © 1998 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 1998 Softcover reprint of the hardcover 1st edition 1998 All rights reserved. No part ofthis publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission ofthe publisher, SpringerScience+Business Media, LLC.
Printed on acid-free paper.
Contents
Series Foreword
xiii
Contributing Authors
xv
Introduction: The Real Contribution of Fuzzy Systems
1
Didier Dubois, Hung T. Nguyen, Henri Prade, and Michio Sugeno
References 1 Methodology of Fuzzy Control
14
19
Hung T. Nguyen and Vladik Kreinovich
1.1
Introduction: Why Fuzzy Control 1.1.1 Traditional control methodology and its limitations 1.1.2 What we can use instead of the classical control model 1.2 How to Translate Fuzzy Rules into the Actual Control: General Idea 1.3 Membership Functions and Where They Come From 1.4 Fuzzy Logical Operations 1.5 Modeling Fuzzy Rule Bases 1.6 Inference From Several Fuzzy Rules 1.7 Defuzzification 1.8 The Basic Steps of Fuzzy Control: Summary 1.9 Tuning 1.10 Methodologies of Fuzzy Control: Which Is The Best? References 2 Introduction to Fuzzy Modeling
19
20 23 25 28 38 43 46 49 51 51 53 59 63
Kazuo Tanaka and Michio Sugeno
2.1
Introduction
63
vi
FUZZY SYSTEMS:
MODELING AND CONTROL
2.2 2.3
Takagi-Sugeno Fuzzy Model Sugeno-Kang Method 2.3.1 Structure identification 2.3.2 Prediction of water flow rate in the river Dniepr 2.4 SOFIA 2.4.1 Algorithm 2.4.2 Prediction of CO concentration at a traffic intersection 2.4.3 Prediction of O2 concentration in a municipal refuse incinerator 2.5 Conclusion References 3 Fuzzy Rule-Based Models and Approximate Reasoning
64 65 65 69 69 70 79 81 84 87 91
Ronald R. Yage1' and Dimita1' P. Filev
3.1 Introduction 3.2 Linguistic Models 3.3 Inference with Fuzzy Models 3.4 Mamdani (Constructive) and Logical (Destructive) Models 3.5 Linguistic Models With Crisp Outputs 3.6 Multiple Variable Linguistic Models 3.7 Takagi-Sugeno-Kang (TSK) Models 3.8 A General View of Fuzzy Systems Modeling 3.9 MICA Operators 3.10 Aggregation in Fuzzy Systems Modeling 3.11 Dynamic Fuzzy Systems Models 3.12 TSK Models of Dynamic Systems 3.13 Conclusion References 4
Fuzzy Rule Based Modeling as a Universal Approximation Tool
91 92 93 95 103 105 112 113 114 115 12
