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Integration of Fuzzy Logic and Chaos Theory
Zhong Li, Wolfgang A. Halang, Guanrong Chen (Eds.)
Integration of Fuzzy Logic and Chaos Theory
Studies in Fuzziness and Soft Computing, Volume 187
Editor-in-chief
Prof. Janusz Kacprzyk
Systems Research Institute
Polish Academy of Sciences
ul. Newelska 6
01-447 Warsaw
Poland
E-mail: kacprzyk@ibspan.waw.pl
Further volumes of this series
can be found on our homepage:
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Vo l . 186. Radim Belohlávek, Vilém
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Integration of Fuzzy Logic and Chaos
Theory, 2006
ISBN 3-540-26899-5
springer.com
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Vo l . 174. Mircea Negoita, Daniel Neagu,
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Vo l . 175. Anna Maria Gil-Lafuente
Fuzzy Logic in Financial Analysis, 2005
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Vo l . 176. Udo Seiffert, Lakhmi C. Jain,
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Bioinformatics Using Computational
Intelligence Paradigms, 2005
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Vo l . 177. Lipo Wang (Ed.)
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Vo l . 178. Claude Ghaoui, Mitu Jain,
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Vo l . 179. Mircea Negoita,
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Real World Applications of Computational
Intelligence, 2005
ISBN 3-540-25006-9
Zhong Li
Wolfgang A. Halang
Guanrong Chen
(Eds.)
Integration of Fuzzy Logic
and Chaos Theory
ABC
Dr. Zhong Li
Professor Wolfgang A. Halang
Professor Guanrong Chen
Department of Electronic Engineering
City University of Hong Kong
Tat Chee Avenue, Kowloon
Hong Kong/PR China
E-mail: gchen@ee.cityu.edu.hk
FernUniversität in
Hagen
FB Elektrotechnik
Postfach 940, 55084 Hagen
Germany
E-mail: zhong.li@fer_n_uni-hagen.de
wolfgang.halang@fernuni-hagen.de
Library of Congress Control Number: 2005930453
ISSN print edition: 1434-9922
ISSN electronic edition: 1860-0808
ISBN-10 3-540-26899-5 Springer Berlin Heidelberg New York
ISBN-13 978-3-540-26899-4 Springer Berlin Heidelberg New York
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
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liable for prosecution under the German Copyright Law.
Springer is a part of Springer Science+Business Media
Springer-Verlag Berlin Heidelberg 2006
Printed in The Netherlands
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c
Preface
The 1960s were perhaps a decade of confusion, when scientists faced di -
culties in dealing with imprecise information and complex dynamics. A new
set theory and then an infinite-valued logic of Lotfi A. Zadeh were so con-
fusing that they were called fuzzy set theory and fuzzy logic; a deterministic
system found by E. N. Lorenz to have random behaviours was so unusual
that it was lately named a chaotic system. Just like irrational and imaginary
numbers, negative energy, anti-matter, etc., fuzzy logic and chaos were grad-
ually and eventually accepted by many, if not all, scientists and engineers as
fundamental concepts, theories, as well as technologies.
In particular, fuzzy systems technology has achieved its maturity with
widespread applications in many industrial, commercial, and technical fields,
ranging from control, automation, and artificial intelligence to image/signal
processing, pattern recognition, and electronic commerce. Chaos, on the other
hand, was considered one of the three monumental discoveries of the twentieth
century together with the theory of relativity and quantum mechanics. As a
very special nonlinear dynamical phenomenon, chaos has reached its current
outstanding status from being merely a scientific curiosity in the mid-1960s
to an applicable technology in the late 1990s.
Finding the intrinsic relation between fuzzy logic and chaos theory is
certainly of significant interest and of potential importance. The past 20 years
have indeed witnessed some serious explorations of the interactions between
fuzzy logic and chaos theory, leading to such research topics as fuzzy modeling
of chaotic systems using Takagi–Sugeno models, linguistic descriptions of
chaotic systems, fuzzy control of chaos, and a combination of fuzzy control
technology and chaos theory for various engineering practices.
A deep-seated reason to study the interactions between fuzzy logic and
chaos theory is that they are related at least within the context of human
reasoning and information processing. In fact, fuzzy logic resembles human
approximate reasoning using imprecise and incomplete information with in-
accurate and even self-conflicting data to generate reasonable decisions under
such uncertain environments, while chaotic dynamics play a key role in human
brains for processing massive amounts of information instantly. It is believed
that the capability of humans in controlling chaotic dynamics in their brains
is more than just an accidental by-product of the brain’s complexity, but

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