Fuzzy Modelling Paradigms and Practice
Fuzzy Modelling: Paradigms and Practice provides an up-to-date and authoritative compendium of fuzzy models, identification algorithms and applications. Chapters in this book have been written by the leading scholars and researchers in their respective su
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Paradigms and Practice
INTERNATIONAL SERIES IN INTELLIGENT TECHNOLOGIES
Prof. Dr. Dr. h.c. Hans-Jiirgen Zimmermann, Editor European Laboratory for Intelligent Techniques Engineering Aachen, Germany Other books in the series:
Applied Research in Fuzzy Technology by Anca L. Ralescu
Analysis and Evaluation of Fuzzy Systems by Akira Ishikawa and Terry L. Wilson
Fuzzy Logic and Intelligent Systems edited by Hua Li and Madan Gupta
Fuzzy Set Theory and Advanced Mathematical Applications edited by Da Ruan
Fuzzy Databases: Principles and Applications by Frederick E. Petry with Patrick Bose
Distributed Fuzzy Control of Multivariable Systems by Alexander Gegov
FUZZY MODELLING Paradigms and Practice
edited by
Witold Pedrycz
University of Manitoba, Canada
.., ~
KLUWER ACADEMIC PUBLISHERS Boston / Dordrecht / London
Distributors for North America: Kluwer Academic Publishers 101 Philip Drive Assinippi Park Norwell, Massachusetts 02061 USA
Distributors for all other countries: Kluwer Academic Publishers Group Distribution Centre Post Office Box 322 3300 AH Dordrecht, THE NETHERLANDS
Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-13: 978-1-4612-8589-2 e-ISBN-13: 978-1-4613-1365-6 DOl: 10.1007/978-1-4613-1365-6
Copyright
1996 by Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 1996 ©
All rights reserved. No part of this 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 of the publisher, Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norwell, Massachusetts 02061
Printed on acidlree paper.
CONTENTS EDITOR'S PREFACE
XVll
PART 1: MODELLING WITH FUZZY SETS 1.1. FUZZY MODELS: METHODOLOGY, DESIGN, APPLICATIONS, AND CHALLENGES W Pedrycz 1.
INTRODUCTORY COMMENTS
2. 3. 4. 5.
A GENERAL TOPOLOGY OF FUZZY MODELS
3 5
FUZZY ENCODING AND DECODING
6
DESIGN OF LOSSLESS COMMUNICATION CHANNELS
9
CLASSES OF FUZZY MODELS
10
6.
VERIFICATION AND VALIDATION OF FUZZY MODELS
18
7. 8.
CONCLUSIONS
20 21
REFERENCES
PART 2: RELATIONAL MODELS 2.1.
FUNDAMENTALS OF FUZZY RELATIONAL CALCULUS S. Gottwald
1.
FUZZY RELATIONS
2.
PROPERTIES OF FUZZY RELATIONS
25 32
3. 4.
RELATIONAL EQUATIONS AND FUZZY CONlROL
38
REFERENCES
46
vi
2.2.
MAX-MIN RELATIONAL NETWORKS A. Blanco, M. Delgado, I. Requena
1.
INTRODUCTION
49
2.
MODELS OF (FUZZY) SYSTEMS
50
3.
IDENTIFICATION OF FUZZY RELATIONAL EQUATIONS BY FUZZY NETWORKS WITHOUT ACTIVATION FUNCTION
4.
EXPERIMENTAL COMPARATIVE STUDIES
56 67
5.
REFERENCES
68
2.3.
RELATIONAL CALCULUS IN DESIGNING FUZZY PETRI NETWORKS H. Scarpelli, F. Gomide
1.
INTRODUCTION
71
2. 3. 4.
THE HIGH LEVEL FUZZY PE1RI NET MODEL HLFPN AND RELATIONAL EQUATIONS THE ROLE OF RELATIONAL EQUATIONS IN BACKWARD REASONING
73
84
CONCLUSIONS REFERENCES
87 87
5. 6.
81
2.4. PREDICTION IN RELATIONAL MODELS J. Valente
