Table Of ContentFuzzy 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: [email protected]
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: [email protected]
m. [email protected]
[email protected]
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)
DOI 10.1007/978-3-7908-1841-3
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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 per
ceived 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 con
trol 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 in
dustrial 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 ap
plications, ad hoc solutions, "quick and dirty" tools and techniques, etc. that are usu
ally effective and efficient for solving practical problems. This does not mean that as
pects of practical implementations should not be accounted for by scholars and re
searchers.
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 promi
nent scientists, Professors Zadeh, Peschel and the editors, that present remarks and vi
sions 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 gen
eral 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 non
fuzzy 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 re
lated 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 my
self. 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 applica
tions 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 be
come leading experts in both theory and applications. Notable examples were here re
sults 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 Ger
many 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 inter
ested 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 (IP M) at the University of
ZittaulG6rlitz. Nowadays we can resume with gratification that this meeting has al
ready 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 con
trol 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 devel
oped 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 enginee
ring).
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 Control
lers 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 uni
versities, institutions, and industry in the areas of teaching, research, and development
between Eastern and Western European countries; also basing on the "three-countries
corner" built by Poland, Czech Republic and Germany, or broader, between Eastern
and Western countries. These ambitions have permanently been encouraged by Pro
fessor 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 University of Applied Sciences
Michael Wagenknecht Ziuau/G6rlitz
Nasredin Chaker
Contents
Introductory Sections
From Computing with Numbers to Computing with Words -From Mani 3
pulation of Measurements to Manipulation of Perceptions
L. A. Zadeh
Fractal Logics Versus Fuzzy Logics 38
M. Peschel
Knowledge Representation Using Fuzzy Logic Based Characteristics 52
N. Chaker, R. Hampel
Fuzzy Sets Theory
On t-Norms as Basic Connectives for Fuzzy Logic 77
S. Gottwald
Generalized Parametric Conjunction Operations in Fuzzy Modeling 88
I. Batyrshin
The Equality of Inference Results Using Fuzzy Implication and Conjunc 98
tive Interpretations of the If Then Rules Under Defuzzijication
E. Czogala, N. Henzel, I. Leski
Adaptive Information Systemfor Multivariate Data Approximation Prob 109
lems
W. Kosinski, M. Weigl
FGCounts of Fuzzy Sets with Triangular Norms 121
M. Wygralak, D. Pilarski
On the Approximate Solution of Fuzzy Equation Systems 132
M. Wagenknecht, V. Schneider, R. Hampel
x
Using Fuzzy Parasets in Problem-Solving Under Uncertainty 142
J. Sajda
On the Change of the Distribution Shape of Randomized Fuzzy Vari 154
ables by Filtering Over Compatibilty Degrees
J. G. Sustal
On Optimization with Fuzzy Constraint Conditions 166
J. Liu, D. Ruan, Z. Song, Y. Xu
Fuzzy Control Theory
Inforence Methodsfor Partially Redundant Rule Bases 177
R. Mikut, J. Jlikel, L. Groll
Analysis and Design of Fuzzy PID Controller Based on Classical PID 186
Controller Approach
P. Pivonka
Expert Methods in the Theory ofA utomatic Control 200
v. Rotach
Comparative Analysis ofC lassical and Fuzzy PID Algorithms 206
E. Arakeljan, M. Panko, V. Usenko
Non-Fuzzy Knowledge-Rule-Based Controllers and their Optimisation by 213
Means ofG enetic Algorithms
I. Sekaj
A New Method of Fuzzy Petri Net SyntheSiS and its Application for Con 222
trol Systems Design
J. Kluska, L. Gniewek
