FUZZY LOGIC

FOUNDATIONS

AND INDUSTRIAL

APPLICATIONS

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 Practices by Witold Pedrycz

FUZZY LOGIC FOUNDATIONS

AND INDUSTRIAL APPLICATIONS

EDITED BY

Oa Ruan Belgian Nuclear Research Centre (SCK' CEN)

KLUWER ACADEMIC PUBLISHERS Boston/London/Dordrecht

Mol, Belgium

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.

ISRN-13: 978-1-4612-8627-1 e-I SRN-13; 978-1-461 3-1441-7 001: 10.1007/978-1-4613-1441-7

Copyright © 1996 by Kluwer Academic Publishers

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 pennission of the publisher, Kiuwer Academic Publishers, tol Philip Drive, Assinippi Park, Norwell, Massachusetts 02061

Primed on acid-free paper.

to Hans-jurgen Zimmermann

for 25 years of contribution

to fuzzy logic theory and applications

CONTENTS

CONTRIBUTORS

FOREWORD George]. Klir

EDITOR'S PREFACE Da Ruan

Part 1: FUZZY LOGIC FOUNDATIONS

1 A UNIFIED VIEW OF CASE BASED REASONING AND FUZZY MODELING Ronald R. Yager 1 Introduction 2 Fuzzy systems modeling 3 Case based reasoning 4 Solution composition 5 Reinforcement learning for process based cases 6 Conclusion REFERENCES

2 OPEN-MINDEDNESS AND PROBABIUTIES VERSUS POSSmIUTIES

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xv

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5 5 6

8 17

21 23 24

Ellen Risdal 27 1 Fuzzy sets and some of Hans-Jiirgen Zimmermann's con-

tributions 27

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viii Fuzzy Logic Foundations and Industrial Applications

2 Two aspects of the probability-possibility discussion and the probabilistic fuzzy-settians 29

3 The TEE model for grades of membership 32 4 The connectives in the TEE model 43 5 The law of the excluded middle, idempotency and asso-

ciativity 48 6 Conclusion 51 REFERENCES 52

3 FUZZY DERN A TIVES AND FUZZY CAUCHY PROBLEMS USING LP METRIC Menahem Friedman, Ming Ma, and Abraham Kandel 1 Introduction 2 Fuzzy derivatives 3 A first order fuzzy differential equation 4 Examples 5 Concluding remarks REFERENCES

4 ON THE ClASSIFICATION AND THE DEPENDENCIES OF THE ORDERING METHODS

57 57 58 64 69 71 71

Xuzhu Wang and Etienne Kerre 73 1 Classification of the ordering indices 73 2 Brief introduction to the first class of

ordering approaches 76 3 Investigation of existing links between the indices in the

first class of ordering methods 80 4 Concluding remarks 87 REFERENCES 88

Part 2: FUZZY LOGIC SYSTEMS

5 POSSIBILITY MODEL AND ITS APPUCATIONS Hideo Tanaka 1 Introduction 2 Possibility analysis based on fuzzy numbers

93 93 94

Contents ix

3 Possibility analysis based on fuzzy vectors 98 4 Identification method of possibility distributions 102 5 Interval regression analysis 104 6 Concluding remarks 107 REFERENCES 109

6 INTERACTIVE FUZZY PROGRAMMING FOR MULTIOBJECTIVE 0-1 PROGRAMMING PROBLEMS THROUGH GENETIC ALGORITHMS WITH DOUBLE STRINGS Masatoshi Sakawa and Toshihiro Shibano III 1 Introduction 112 2 Interactive fuzzy programming through

genetic algorithms 114 3 Genetic algorithms with double strings 118 4 Multiobjective project selection problems 122 5 Conclusion 125 REFERENCES 125

7 THE HANDLING OF FUZZY OBJECTIVE FUNCTIONS IN (MULTICRITERIA) UNEAR PROGRAMS Heinrich J. Rommelfanger 129 1 Introduction 129 2 The multiobjective approach 130 3 Compromise objective function(s) 132 4 Satisfying solutions 138 5 Conclusions 142 REFERENCES 142

8 MAKING DECISIONS ON FUZZY INTEGER LINEAR PROGRAMMING PROBLEMS Francisco Herrera and Jose Luis Verdegay 147 1 Introduction 147 2 Theoretical results 150 3 An algorithm for PILP problems 152

x Fuzzy Logic Foundations and Industrial Applications

4 Numerical example 155 5 The parametric right-hand-side in 0-1 fuzzy program-

ming problems 156 6 Choosing a solution 158 REFERENCES 162

9 INFORMATION DIFFUSION PRINCIPLE AND APPUCATION IN FUZZY NEURON Chongfu Huang and Da Ruan 165 1 Introduction 165 2 Incompleteness and fuzziness 168 .

3 Information distribution 170 4 Information diffusion principle 177 5 Empirical distribution function, histogram and diffusion

estimator 182 6 Normal information diffusion 184 7 Application in BP neural network 188 8 Conclusion 195 REFERENCES 195

Part 3: FUZZY LOGIC INDUSTRIAL APPLICATIONS

10 SOME APPllCATION EXAMPLES OF FUZZY SET THEORY Hans Hellendoorn 201 1 Introduction 201 2 Automatic transmission control 202 3 The fuzzy washing machine 208 4 The H2-leakage diagnosis system 210 5 Fuzzy traffic technology 215 6 Fuzzy logic in telecommunications 218 REFERENCES 224

11 RECENT SUCCESSFUL FUZZY LOGIC APPUCATIONS IN INDUSTRIAL AUTOMATION Constantin von Altrock 225

Contents xi

1 Fuzzy logic in industrial automation 225 2 Merging fuzzy logic and PLCs 228 3 Application case studies 229 4 Conclusions 242 REFERENCES 245

12 FIPS-FOUNDATIONS OF A NEW TOOL FOR PROCESS CONTROL PROBLEMS Siegfried Gottwald and Manfred Locke 247 1 Start-up and shut-down control of industrial plants 247 2 General fundamentals of the system FIPS 250 3 Theoretical basis of the model-building module 254 4 Theoretical background for the logic module 259 REFERENCES 263

13 INDUSTRIAL APPLICATIONS OF FUZZY LOGIC AND NEURAL NETWORKS IN CHINA Xiaozhong Li 265 1 Introduction 265 2 Applications in process controls without a closed loop 266 3 Applications in replacing PID techniques 269 4 Applications in electricity consumers 270 5 An intelligent fuzzy control system 271 6 The future work on fuzzy industrial applications 272 REFERENCES 273

14 THE POTENTIAL OF FUZZY LOGIC APPLICATIONS IN INDUSTRY Arien ]. van der Wal 275 1 Introduction 276 2 Industrial controller design 277 3 Case study: Omron's industrial temperature controller

E5AF 280 4 Case study: overshoot suppression with FL by set-point

scheduling 287 5 Case study: ESI00 industrial controller 289

xii Fuzzy Logic Foundations and Industrial Applications

6 Case study: control of a sintering oven 293 7 Combining fuzzy control with other methods 296 8 Stability and robustness of fuzzy controllers 299 9 Sensor fusion 301 10 Case study: fuzzy human detector 303 11 Case study: fuzzy pattern recognition: earthquake sen-

sor 305 12 Case study: the HMS expert system 308 13 Conclusions 309 REFERENCES 311

15 FUZZY LOGIC APPliCATIONS IN NUCLEAR INDUSTRY Da Ruan 313 1 Introduction 313 2 Current trends in nuclear research 316 3 Fuzzy logic applications in nuclear engineering 318 4 Concluding remarks 321 REFERENCES 321

SUBJECT INDEX 329

Constantin von Altrock Inform GmbH Aachen, Germany

Menahem Friedman Physics Dept NRCN Beer-Sheva, Israel

Siegfried Gottwald Inst. fUr Logik und Wissenschaftstheorie UniversWit Leipzig Leipzig, Germany

Hans Hellendoorn Siemens AG Munich, Germany

Francisco Herrera Dept of CS and Artificial Intelligence University of Granada Granada, Spain

Ellen Hisdal Institute of Informatics University of Oslo Oslo, Norway

Chongfu Huang Dept of Resources and Environm. Science Beijing Normal University Beijing, China

CONTRIBUTORS

Abraham Kandel Computer Science and Engineering Dept University of South Florida Tampa, Florida, USA

Etienne Kerre Dept of Applied Mathematics and CS University of Gent Gent, Belgium

Xiaozhong Li Institute of Computing Chinese Academy of Science Beijing, P.R. China

Manfred Locke Ingenieurbiiro Locke Leipzig, Germany

MingMa Harbin Institute of Technology Harbin, P. R. China

Heinrich J. Rommelfanger Institute of Statistics and Mathematics J. W. Goethe-University Frankfurt am Main, Germany

DaRuan Fuel Research Unit Nuclear Research Centre (SCK' CEN) Mol, Belgium

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Masatoshi Sakawa Dept of Industrial and Systems Eng. Hiroshima University Higashi-Hiroshima, Japan

Toshihiro Shibano Shinryo Corporation Yokohama, Japan

Hideo Tanaka Dept of Industrial Engineering Osaka Prefecture University Osaka, Japan

Jose Luis Verdegay Dept of CS and Artificial Intelligence University of Granada Granada, Spain

Arien J. van der Wal Omron Electronics B.V. Eindhoven, The Netherlands

XuzhuWang Dept of Applied Mathematics and CS University of Gent Gent, Belgium

Ronald R. Yager Machine Intelligence Institute lona College New Rochelle, New York, USA

Contributors

FOREWORD

For anyone interested even to a small degree in foundations or applications of fuzzy logic in its broad sense, as a system of concepts, principles, and methods for dealing with modes of reasoning that are approximate rather than exact, it is virtually impossible not to come across at least some con­tributions of Professor Hans Zimmermann to this field. He is undoubtedly one of the earliest and most significant contributors to fuzzy set theory, upon which fuzzy logic in its broad sense is based.

It is significant that his contributions to fuzzy set theory and fuzzy logic are not only scholarly, but also organizational and educational. To cover these contributions in detail is far beyond the scope of this foreword. I can only try to capture the essence of his enormous contributions to each of these areas.

Hans began his research in fuzzy set theory around the mid 1970s, driven primarily by his belief that the use of fuzzy sets in decision making would make it more realistic and practicable. One of his early contributions to fuzzy set theory was a formulation and analysis of fuzzy linear program­ming. This was followed over the years by many other contributions he made to the emerging area -of fuzzy decision making. Another of his early contributions was a collection of empirical studies regarding the construc­tion of membership functions of fuzzy sets and operations on fuzzy sets. This empirical research resulted in a formulation of a parametrized fam­ily of operations, which allows one to choose an appropriate operation in each particular application context. These results initiated a new branch of research in fuzzy set theory, which is particularly important for appli­cations. In addition to his extensive research on fuzzy decision making and his empirical research, Hans has also made significant contributions to several other areas involving fuzzy sets and fuzzy logic, including fuzzy expert systems, fuzzy control, and fuzzy data analysis.

Organizational contributions made by Hans to the emerging areas of fuzzy set theory, fuzzy logic, and fuzzy systems are as impressive as his schol-

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arly contributions to these areas. Among these, three contributions are particularly significant: in 1978, Hans initiated the journal Fuzzy Sets and Systems, which has evolved under his capable editorship into a principal journal covering basic and applied research in the areas of fuzzy set the­ory, fuzzy logic, and fuzzy systems; in 1984, Hans was the key player in forming the International Fuzzy Systems Association (IFSA), an important professional organization, which serves now as a Federation of national, regional, and other relevant organizations; in 1993, Hans initiated a major annual conference in Europe, The European Congress on Fuzzy and Intel­ligent Technologies (EUFIT), which turned out to be highly successful.

In the sphere of education, Hans is recognized as one of the earliest promot­ers of education in fuzzy set theory. In 1985, his book Fuzzy Set Theory and Its Applications was published, and it was quickly recognized as the first book on the subject that possessed all the characteristics of a text­book. The book has become a classic of fuzzy set literature and has helped to initiate courses on the subject at numerous universities, particularly in the areas of business administration, management, operations research, engineering, and computer science. A revised and enlarged second edition of the text was published in 1991. Another excellent textbook written by Hans, focusing more on application of fuzzy sets in decision making and expert systems, was published under the title Fuzzy Sets, Decision Making and Expert Systems in 1987. Both textbooks are based on several courses Hans himself developed and taught at his home university, The Institute of Technology in Aachen, Germany, as well as at other universities. He also presented tutorials on various topics associated with fuzzy sets and fuzzy logic at numerous conferences and on other occasions.

Dr Ruan deserves our gratitude and congratulations for designing and edit­ing this excellent book, and dedicating it to Professor Hans-Jiirgen Zimmer­mann-a distinguished scholar, educator, and organizer-for his enormous contributions to the field of fuzzy set theory. Since the book is coauthored by some of the most important contributors to this field, it is a proper tribute to this distinguished member of the fuzzy set cOIIllllunity.

George 1. Klir Binghamton, New York, May 1996

EDITOR'S PREFACE

This book is a congratulatory volume dedicated to Professor Hans-Jili'gen Zimmermann on the occasion of his 25 years of contribution to fuzzy logic theory and applications at the University of Aachen (the Technische Hochschule Aachen), Germany.

At the beginning of 1970, in cooperation with the University of Aachen, Professor Zimmermann established the European Working Group on Fuzzy Sets, the first institutionalized group doing research in the area of fuzzy technology. Professor Zimmermann, as the Editor-in-Chief of the Inter­national Journal of Fuzzy Sets and Systems, together with Professor Lotfi Zadeh, the Honorary Editor, have been with the oldest and most estab­lished journal in its field as from its start in 1978. They have both played a pioneer's role in making fuzzy logic an academic discipline.

Professor Zimmermann has spent approximately 10 years in practise in different functions and companies before he entered his university career. He has been awarded the first "Euro Gold Medal" (highest distinction in operations research in Europe), the "K.S. Fu Certificate of Appreciation" (highest distinction of the North American Fuzzy Information Processing Society) and the Moisil Prize and Gold Medal for outstanding contributions to the theory and applications of fuzzy systems (Romania). He has also received a Doctorate Honoris Causa from the Free University of Brussels.

Professor Zimmermann is heavily involved in research and in the applica­tions of fuzzy technology, especially in industry, banking, and public ad­ministration. He has published almost 200 papers and 23 books (in English and in German) in the areas of operations research, decision theory, and fuzzy set theory. He is the scientific Director of ELITE (European Laboratory for Intelligent Techniques Engineering) and formed the companies INFORM and MIT, where he now supervises a number of industrial projects which apply fuzzy logic to industrial problems. He is also the Chairman of the Department of Operations Research at the Aachen Institute of Technology.

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I already knew the name of Professor Zimmermann a long time before I began my PhD thesis on fuzzy logic. But the very first time I met Profes­sor Zimmermann was in December 1990 at the University of Gent where I defended my thesis. Professor Zimmermann was a member of my PhD committee (among other members were Professor Philippe Smets, Profes­sor Etienne Kerre, and seven other mathematics professors). Since then, I have benefited from a close collaboration with Professor Zimmermann. During IFSA'93 in Seoul, I kindly asked for his advice for establishing the new international forum FLINS (Fuzzy Logic and Intelligent technologies in Nuclear Science). To my surprise, he positively supported this very idea and agreed to serve as the Chairman of the international scientific advisory committee. At EUFIT'93 in Aachen, I discussed the detailed plan of FLINS'94 (the first international FUNS workshop) with him. During FLINS'94 in Mol, he introduced the principles of fuzzy logic and intelligent technologies to engineers and nuclear scientists in his opening lecture. After FLINS'94, he very kindly offered us a special issue on "Nuclear Engineering" of Fuzzy Sets and Systems for 15 selected papers presented at FLINS'94. In 1995, he con­tributed a foreword to FLINS Volume 4, "Fuzzy Set Theory and Advanced Mathematical Applications." That volume was dedicated to Professor Eti­enne Kerre and published in Professor Zimmermann's International Series in Intelligent Technologies by Kluwer Academic Publishers. For FLINS'96 (the second international FUNS workshop), Professor Zimmermann pre­pared his new contribution as opening lecture on "Fuzzy algorithmic and knowledge-based decision support in nuclear engineering."

I am very pleased to edit, on behalf of FUNS, this book on Fuzzy Logic Foundations and Industrial Applications in the International Series in Intel­ligent Technologies in honor of Professor Hans-JOrgen Zimmermann. The primary aims of this volume were to celebrate Professor Zimmermann's 25 years of contribution to fuzzy logic theory and applications, and to provide researchers and engineers from both academic and industry with up-to-date coverage of new results on fuzzy logic and its industrial applica­tions. I hence informed Professor Zimmermann of this project at IFSA'95 in Sao Paulo. This issue consists of a collection of chapters written by his friends and disciples only (basic theory, fuzzy linear programming and multicriteria analYSiS, and applications). Due to the limitations of time and space, unfortunately, it has not been possible to include in this volume all the contributions submitted or promised by Professor Zimmermann's friends (in particular those of Professor Lotfi Zadeh, Professor John Yen, and Professor Burhan TOrksen).

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This book is divided into three logical parts, coinciding with Professor Zim­mermann's areas. In the first part, entitled Fuzzy Logic Foundations and starting with a dedication to Hans-jiirgen Zimmermann, Professor Yager presents a unified view of case-based reasoning and fuzzy modeling; after a brief introduction of fuzzy sets and some of Professor Zimmermann's contributions, Professor Hisdal describes a probabilistic interpretation of grades of membership; Professor Kandel et al. introduce a new approach for defining a fuzzy derivative, a first-order fuzzy differential equation, and a fuzzy Cauchy problem; and Professor Kerre and his co-worker Wang classify all the approaches to order fuzzy quantities and investigate some dependencies of the ordering methods. In the second part, Fuzzy Logic Systems, Professor Tanaka gives some basic principle of possibility model and its applications; Professor Sakawa et al. propose interactive fuzzy pro­gramming for multiobjective 0-1 programming problems through genetic algorithms with double strings; Professor Rommelfanger gives a critical survey on the handling of fuzzy objective functions in (multicriteria) linear programmes; Professor Verdegay and his co-author Herrera discuss mak­ing decisions on fuzzy integer linear programming problems, and the fifth contribution in this part by Huang and Ruan presents information diffusion principle and application in fuzzy neuron. In the last part. Fuzzy Logic In­dustrial Applications, Hellendoorn describes four fuzzy logic applications at Siemens; von Altrock reviews eight recent successful applications of fuzzy logic in industrial automation; Professor Gottwald and his co-author Locke introduce foundations of a new tool of a fuzzy instrumented process control system for process control problems; Li shortly presents industrial applications of fuzzy logic and neural networks in China; van der Wal gives an overview on the potential of fuzzy logic applications in industry, and finally Ruan briefly reports on the current fuzzy logic applications in nu­clear industry. Each chapter of the issue is self-contained and I hope this volume will benefit many readers around the world.

Special thanks are due to Professor George Klir for his willingness to write a foreword for this issue; to all the other authors and contributors for their kind cooperation to this book; to Alexander Greene (Publisher, Kluwer Aca­demic Publishers) for his kind advice and help to publish this volume, to jL Doumont UL consulting. Brussels) for his proofreading of parts of the manuscript and his final typesetting of this book, and to the Belgian Nuclear Research Centre for its support.

DaRuan Mol, june 1996