Fuzzy Control

Advances in Soft Computing Editor-in-cbief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw, Poland E-mail: kacprzyk@ibspan.waw.pl http://www.springer.delcgi-binlsearch-bock.pl?series=4240

Esko Turunen Mathemalics Behind Fuzzy Logic 1999. ISBN 3-7908-1221-8

Robert Fuller Introduction to Neuro-Fuzzy Systems 2000. ISBN 3-7908-1256-0

Robert John and Ralph Birkenhead (Eds.) Soft Computing Techniques and Applications 2000. ISBN 3-7908-1257-9

Mieczyslaw Klopotek, Maciej Michalewicz and Slawomir T. Wierzchon (Eds.) Intelligent Information Systems 2000. ISBN 3-7908-1309-5

Peter Sincak, Jan VaScak, Vladimir Kvasnicka, and Radko Mesiar (Eds.) The State of the Art in Computational Intelligence 2000. ISBN 3-7908-1322-2

Rainer Hampel Michael Wagenknecht N asredin Chaker (Eds.)

Fuzzy Control Theory and Practice

With 207 Figures and 33 Tables

Springer-Verlag Berlin Heidelberg GmbH

Prof. Dr. Rainer Hampel Dr. Michael Wagenknecht Dr. Nasredin Chaker University of Applied Sciences ZittaulGorlitz Institute of Process Technique, Automation and Measuring Technique (!PM) Theodor-Korner-Allee 16 02763 Zittau Germany E-mail: r.hampel@htw-zittau.de

m. wagenknecht@htw-zittau.de n.chaker@htw-zittau.de

ISSN 1615-3871 ISBN 978-3-7908-1327-2

Die Deutsche Bibliothek - CIP-Einheitsaufnahme Fuzzy control: with 33 tables 1 Rainer Hampel, Michael Wagenknecht, Nasredin Chaker (eds.). -Springer-Verlag Berlin Heidelberg 2000

(Advances in soft computing) ISBN 978-3-7908-1327-2 ISBN 978-3-7908-1841-3 (eBook)

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© Springer-Verlag Berlin Heidelberg 2000 Originally published by Physica-Verlag Heidelberg in 2000

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Softcover Design: Erich Kirchner. Heidelberg

SPIN 10776205 88/2202-5 4 3 2 I 0 - Printed on acid-free paper

DOI 10.1007/978-3-7908-1841-3

Foreword

The present edited volume is of special importance, and for various reasons. First of all, it is one of the most comprehensive and multifaceted coverage of broadly per­ceived fuzzy control in the literature. The editors have succeeded to collect papers from leading scholars and researchers on various subjects related to the topic of the volume. What is relevant and original is that - as opposed to so many volumes on fuzzy control published by virtually all major publishing houses that are strongly technically oriented and covering a narrow spectrum of issues relevant to fuzzy con­trol itself - the editors have adopted a more general and far sighted approach.

Basically, the perspective assumed in the volume is that though fuzzy control has reached such a level of maturity and implementability that it has become a part of in­dustrial practice, science and academic research still have a relevant role to play in this area. One should however take into account that by their very nature, the role of science and academic research is very peculiar and going beyond straightforward ap­plications, ad hoc solutions, "quick and dirty" tools and techniques, etc. that are usu­ally effective and efficient for solving practical problems. This does not mean that as­pects of practical implementations should not be accounted for by scholars and re­searchers.

The above perspective, maybe even a rationale, has been very well reflected in this edited volume. The editors have found a very good balance between, on the one hand, conceptual and theoretical aspects, and tools and techniques that are relevant for broadly perceived fuzzy control, and on the other hand, on more practical aspects. Moreover, they have attracted prominent contributors whose original works are highly regarded in the field.

The volume starts with an introductory part with more general papers by promi­nent scientists, Professors Zadeh, Peschel and the editors, that present remarks and vi­sions on paradigms which may be of general relevance to broadly perceived fuzzy technology, notably fuzzy control. These include computing with words, relations between fuzzy and other logics, and a relevant and general issue of the use of fuzzy logic in knowledge representation that is a key issue for intelligent systems in general.

The second part contains papers on theoretical aspects of fuzzy sets and possibility theories, including aggregation operators, logical operators, fuzzy inference, fuzzy equations and their solution, fuzzy optimization, etc. These papers concern more gen­eral issues, maybe not directly related to narrowly meant fuzzy control, but whose general character is relevant from a broader perspective.

The third part contains papers directly related to fuzzy control including those on the theory of fuzzy control, rule bases and inference for fuzzy controllers, the use of Petri nets for the design of control systems, comparative analyses of fuzzy and non­fuzzy controllers, etc.

The fourth part is concerned with applications of fuzzy tools, notably of fuzzy control, and includes both technological application as, e.g., in process control, and non-technological ones as, e.g., in medical diagnosis and social sciences.

VI

The fifth part discusses various aspects of hybrid approaches, including elements of fuzzy logic, neural networks and evolutionary computation. Both general issues re­lated to, e.g., proper architectures of hybrid systems or inference schemes, and applied aspects are dealt with.

The last part of the volume contains various papers on the theory and applications of fuzzy tools and techniques in modeling, forecasting and prediction, monitoring and fault diagnosis, decision making and planning, etc. These areas will certainly gain more and more relevance in the future.

While trying to assess this volume one should also emphasize the following fact. The volume may be viewed as a natural consequence of a series of Fuzzy Colloquia that have been held in Zittau (Germany) for some years, with the eight to come in 2000. Initiated as a small local scientific gathering of scholars and researchers from the neighboring regions of Germany, Poland and the Czech Republic, they have soon become a larger, more global scientific event attracting more and more prominent people from all parts of the world. This is an unquestionable achievement of Professor Hampel, and his collaborators, notably the two other editors of this volume, Dr. Wagenknecht and Dr. Chaker.

The success of Fuzzy Colloquia is also no surprise to many people, including my­self. One should bear in mind that long before the reunification of Germany, in the former German Democratic Republic, research in fuzzy sets theory and its applica­tions was flourishing. Professor Manfred Peschel, then an influential official in the Academy of Sciences, had quite early discovered huge potentials of that new field. He was, and still is, a man of great knowledge, vision and enthusiasm, and had attracted many collaborators, including his younger disciples. These people had quickly be­come leading experts in both theory and applications. Notable examples were here re­sults by, say, Professors Gottwald and Bandemer in more theoretical areas, on the one hand, and Professors Hampel, Bocklisch, Wagenknecht, Straube, Lippe, etc. in more applied areas; I hope that other friends whose names were here omitted would forgive me for this. From this perspective, it is no surprise that since most of these people are still very active, and now have new young and talented disciples, research in fuzzy sets and related areas (e.g., neural networks, evolutionary computation, etc.) in that part of Germany is now very intensive and successful too. And further, the success of the Zittau Colloquia is naturally implied by the fact that it is organized by Professor Hampel together with Dr. Wagenknecht and Dr. Chaker, and that a considerable part of participants consists of people from leading centers from the Eastern lands of Ger­many headed by people I have just mentioned above.

To summarize this short foreword, I would like to congratulate Professor Hampel, Dr. Wagenknecht and Dr. Chaker, the editors of this volume, for their outstanding editorial work that has resulted in a volume that should be on the shelf of all inter­ested in new trends and developments in broadly perceived fuzzy control, in its basic and applied aspects.

Warsaw, April 2000 Janusz Kacprzyk Editor in chief "Advances in Soft Computing"

Preface

The first Zittau Fuzzy Colloquium took place in 1993 on initiative of Professor Peschel, the then director of the International University Institute in Zittau. This idea was picked up and continued by the staff of the Institute of Process Technique, Process Automation and Measuring Technique (I PM) at the University of ZittaulG6rlitz. Nowadays we can resume with gratification that this meeting has al­ready become a tradition in our academic life.

From the very beginning and first of all, the aim of our activities was to contribute to the dissemination of Fuzzy Logic bases and their potentials of application. Starting in 1988, initial works were carried out at the IPM dealing with fuzzy-supported con­trol of combustion in a heating power plant with raw lignite firing. In consequence of the rapid development of computing technique and particularly, of the introduction of digital signal processing in process automation, the potentials of application of Fuzzy Logic were significantly increasing. Correspondingly, the Fuzzy Set Theory devel­oped by Prof. Zadeh in 1965 became an independent scientific discipline within automation engineering and information processing.

Regarding the application of Fuzzy Logic in process automation, it seems to be useful to distinguish two fundamental classes:

1. applications with high degree of repetition (e.g. in consumer good engineering, automotive industry);

2. applications with lower degree of repetition (e.g. in energy and process enginee­ring).

In both cases it is important that for open and closed loop control, monitoring, and diagnosis non-algorithmic expert knowledge can be exploited. While in the first case, the scientific expenditure for expert knowledge acquisition and resulting structuring, parameterization, and optimization of Fuzzy signal processing can be very high (without increasing the costs for the product), in the second case one has to count on effective costs because of problems complexity. From it the following conclusions can be drawn:

- For the second class mentioned above, tools for structuring, parameterization and optimization must be developed that can compete with classical design methods.

- Experiences from classical signal processing have to be implemented. They play the role of quality criteria.

That is why a large number of publications deal with the design of Fuzzy Control­lers having PID-similar behaviour.

VIII

The present volume subdivides into the following chapters

Introductory Sections Fuzzy Sets Theory Fuzzy Control Theory Fuzzy Control Application Neuro Fuzzy Systems and Genetic Algorithms Diagnosis, Monitoring, and Decision Support Systems

and the contributions therein are widely ranging in the above discussed problems.

Beside the already mentioned features and due to its particular status, the ZiUau Fuzzy Colloquium has been engaging in the promotion of cooperation between uni­versities, institutions, and industry in the areas of teaching, research, and development between Eastern and Western European countries; also basing on the "three-countries­corner" built by Poland, Czech Republic and Germany, or broader, between Eastern and Western countries. These ambitions have permanently been encouraged by Pro­fessor L. A. Zadeh and other outstanding scientific authorities.

At this place we want to remind of the great engagement and brilliant scientific contributions made by our colleague E. Czogala who died in a tragic accident in October 1998. So, we decided to include one of his earlier conference papers.

The editors would like to express their thanks to all authors, Professor Kacprzyk, and Dr. Bihn for benevolent promotion and support during publishing this volume. Finally, we gratefully acknowledge the generous support by the Saxon State Ministry of Science and Arts (SMWK), and the German Academic Exchange Service (DAAD) which has been one of the decisive pre-conditions for our scientific activities.

March,2000

Rainer Hampel Michael Wagenknecht Nasredin Chaker

University of Applied Sciences Ziuau/G6rlitz

Contents

Introductory Sections

From Computing with Numbers to Computing with Words - From Mani­pulation of Measurements to Manipulation of Perceptions

L. A. Zadeh

Fractal Logics Versus Fuzzy Logics

M. Peschel

Knowledge Representation Using Fuzzy Logic Based Characteristics

N. Chaker, R. Hampel

Fuzzy Sets Theory

On t-Norms as Basic Connectives for Fuzzy Logic

S. Gottwald

Generalized Parametric Conjunction Operations in Fuzzy Modeling

I. Batyrshin

The Equality of Inference Results Using Fuzzy Implication and Conjunc­tive Interpretations of the If Then Rules Under Defuzzijication

E. Czogala, N. Henzel, I. Leski

Adaptive Information Systemfor Multivariate Data Approximation Prob­lems

W. Kosinski, M. Weigl

FGCounts of Fuzzy Sets with Triangular Norms

M. Wygralak, D. Pilarski

On the Approximate Solution of Fuzzy Equation Systems

M. Wagenknecht, V. Schneider, R. Hampel

3

38

52

77

88

98

109

121

132

x

Using Fuzzy Parasets in Problem-Solving Under Uncertainty

J. Sajda

On the Change of the Distribution Shape of Randomized Fuzzy Vari­ables by Filtering Over Compatibilty Degrees

J. G. Sustal

On Optimization with Fuzzy Constraint Conditions

J. Liu, D. Ruan, Z. Song, Y. Xu

Fuzzy Control Theory

Inforence Methodsfor Partially Redundant Rule Bases

R. Mikut, J. Jlikel, L. Groll

Analysis and Design of Fuzzy PID Controller Based on Classical PID Controller Approach

P. Pivonka

Expert Methods in the Theory of Automatic Control

v. Rotach

Comparative Analysis of Classical and Fuzzy PID Algorithms

E. Arakeljan, M. Panko, V. Usenko

Non-Fuzzy Knowledge-Rule-Based Controllers and their Optimisation by Means of Genetic Algorithms

I. Sekaj

A New Method of Fuzzy Petri Net SyntheSiS and its Application for Con­trol Systems Design

J. Kluska, L. Gniewek

142

154

166

177

186

200

206

213

222

Fuzzy Control Applications

Improving Control Behaviour with Set-Point Pre-Processors

P. Vogrin, W. A. Halang

Automation of Process Pretuning by a Fuzzy-Similar Method

E. Arakeljan, V. Usenko

Selection of Mathematics Model for Daily Diagram Prediction According to Box-Jenkins Method

J. Bahlte, B. Chramcov

The Application of Fuzzy Set to Analysis of Cultural Meaning

I. Koyauchi, N. Sano, H. Kadotani, R. Takahashi

Natural Language Input for Fuzzy Diagnosis

N. Sano, R. Takahashi

Neuro-Fuzzy Systems and Genetic Algorithms

Neural Network Architecture of Fuzzy Systems

D. Rutkowska

A Neuro-Fuzzy Inference System Optimized by Deterministic Annealing

1. Leski, E. Czogala

Neuro-Fuzzy Detector for Industrial Process

M. Kowal, 1. Korbicz

Fuzzy Setting ofGA Parameters

R. Matousek, P. Osmera

Self-Learning Fuzzy Models and Neural Models in Environment Predic­tion

G. M. Sandulescu, M. Bistran

XI

231

245

252

259

265

277

287

294

302

313

XII

Fuzzy Stochastic Multistage Decision Process with Implicitly Given Ter­mination Time

K. Weber, Z. Sun

Diagnosis, Monitoring, and Decision Support Systems

Fuzzy Time Series Analysis

S1. F. Bocklisch, M. PaBler

Fuzzy Modelling of Heart Rate Variability

J. Bila, P. Zitek, P. Kuchar

Fuzzy Approach to Combining Parallel Experts Response

A. Marciniak

Fuzzy Modeling of Dynamic Non-Linear Processes - Applied to Water Level Measurement

A. Traichel, W. Kastner, R. Hampel

Fuzzy Modelling of Multidimensional Non-linear Processes - Design and Analysis of Structures

A. Pieczynski, W. Kastner

Fuzzy Modeling of Uncertainty in a Decision Support System for Electric Power System Planning

1. o. Egwaikhide

Application of the FSOM to Machine Vibration Monitoring

1. Jossa, U. Marschner, W.-J. Fischer

Near-Term Forecasting of Drilling Cost of Borehole by Fuzzy Logic

G. Sementsov, I. Chigur, I. Fadeeva

318

331

346

354

361

376

387

397

406