Fuzzy Systems Engineering: Theory and Practice

233 Pages·2005·5.846 MB·English

by  N. Nedjah, L. de M. Mourelle (auth.), Nadia Nedjah, Luiza de Macedo Mourelle (eds.)

NadiaNedjah,LuizadeMacedoMourelle
FuzzySystemsEngineering
Studiesin Fuzziness andSoft Computing,Volume181
Editor-in-chief
Prof.JanuszKacprzyk
SystemsResearchInstitute
PolishAcademyofSciences
ul.Newelska6
01-447Warsaw
Poland
E-mail:[email protected]
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FuzzySystemsEngineering,2005
ISBN3-540-25322-X
Nadia Nedjah
Luiza de Macedo Mourelle
Fuzzy Systems
Engineering
Theory and Practice
ABC
NadiaNedjah
LuizadeMacedoMourelle
UniversidadedoEstadodoRiodeJaneiro
FaculdadedeEngenharia
RuaSãoFranciscoXavier,524,Sala5022-D
Maracanã,RiodeJaneiro-RJ,20550-900,Brasil
E-mail:[email protected]
[email protected]
LibraryofCongressControlNumber:2005921894
ISSNprintedition:1434-9922
ISSNelectronicedition:1860-0808
ISBN-10 3-540-25322-X SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-25322-8 SpringerBerlinHeidelbergNewYork
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Preface
Whenaskedaboutwhetheracertainaspectisorisnotadequateforinstance,
it is politically incorrect to give a sharp answer, i.e. it is or it is not adequate.
A good politician would answer that the aspect in question is adequate to
some extent but it is also not adequate to another extent. So, if you want to
be a successful politician, you ought to learn fuzzy logic. The mob prefers a
fuzzy answer and sharp minded persons can suffer a great deal in this fuzzy
old world!
Like Politics, computational system modelling is strewn with ambiguous
situations, wherein the designer cannot decide, with precision, what should
betheoutcomeofthesystembecauseofthelackofprecisedataontheactual
situation.LotfiZadeh,aprofessorattheUniversityofCalifornia,usedthefact
that human being do not have always access to precise numerical data, but
they are capable of taking more or less the right the decision with respect to
the situation they are in. The fuzzy theory, as it was first introduced, was an
attempt to yield a new computing paradigm that allow designers to do more
with less. At first, It was embraced in designing feedback controllers as they
could be programmed to accept noisy, imprecise input. Nowadays, the fuzzy
theory, including fuzzy sets, relations, functions and logic, is being exploited,
in all sort of areas and disciplines.
This book is devoted to reporting innovative and significant progress in
fuzzy system engineering. Theoretical as well as practical chapters are con-
templated. The former present original seminal work on improving the fuzzy
theory and the latter exploit it to engineer intelligent systems.
The content of this book is divided in two main parts. The chapters of
the first part present novel developments of the fuzzy theory while those of
the second part describe interesting applications of the fuzzy logic. In the
following,wegiveabriefdescriptionofthemaincontributionofeachofthese
chapters.
VI Preface
Part I: Fuzzy Theory
InChap.1,whichisentitledIntroducingYoutoFuzziness,theauthors,Nadia
Nedjah and Luiza de Macedo Mourelle, introduce fuzzy logic and the
underlying approximate reasoning. First, they present the fuzzy set theory
through their operational semantics. Then, they extend the fuzzy set theory
tofuzzylogic.Inthispurpose,wedefinefuzzypropositionsandrules.Wealso
demonstrate how those are used to reason approximately.
InChap.2,whichentitledA Qualitative Approach for Symbolic Data Ma-
nipulationUnderUncertainty,theauthors,namelyIsis Truck and Herman
Akdag, present a novel a qualitative (also symbolic and linguistic) approach
for knowledge representation. They introduce a qualitative approach to ma-
nipulate uncertainty is as an alternative to classic probabilities and design a
framework that supports the operational semantics of their approach.
In Chap. 3, which entitled Adaptation of Fuzzy Inference System Using
Neural Learning, the author, namely Ajith Abraham, presents three differ-
ent types of cooperative neuro-fuzzy models namely fuzzy associative mem-
ories, fuzzy rule extraction using self-organizing maps and systems capable
of learning fuzzy set parameters. Different Mamdani and Takagi-Sugeno type
integratedneuro-fuzzysystemsarefurtherintroducedwithafocusonsomeof
the salient features and advantages of the different types of integrated neuro-
fuzzy models that have been evolved during the last decade.
Part II: Fuzzy Systems
In Chap. 4, which is entitled A fuzzy approach on guiding model for inter-
ception flight, the author, namely Silviu Ionita, presents an original moving
control model based on the fuzzy logic, applied to some navigation special
issues. The author claim that the steps taken on special flight tasks prove
adequacy of the fuzzy rules based model to this field.
InChap.5,whichisentitledHybridSoftandHardComputingBasedForex
Monitoring Systems, the author, namelyAjith Abraham, attempts to com-
paretheperformanceofhybridsoftcomputingandhardcomputingtechniques
topredicttheaveragemonthlyforexratesonemonthahead.Thesoftcomput-
ing models considered are a neural network trained by the scaled conjugate
gradient algorithm and a neuro-fuzzy model implementing a multi-output
Takagi-Sugeno fuzzy inference system. The author claim that the proposed
hybrid models could predict the forex rates more accurately most of the time
than all the techniques when applied individually.
In Chap. 6, which is entitled On the Stability and Sensitivity Analysis of
Fuzzy Control Systems for Servo-systems, the authors, namely Radu-Emil
Precup and Stefan Preitl,firstpresentthestabilityanalysismethodsded-
icated to fuzzy control systems for servo-systems: the state-space approach,
theuseofPopov’shyperstabilitytheory,thecirclecriterionandtheharmonic
Preface VII
balancemethod.Second,theyperformedthesensitivityanalysisoffuzzycon-
trol systems with respect to the parametric variations of the controlled plant
for a class of servo-systems based on the construction of sensitivity models.
Several case studies are presented.
In Chap. 7, which is entitled Applications of Fuzzy Logic in Mobile Ro-
bots Control, the author, namely Michael Botros, presents two different
approaches for the automatic design of fuzzy inference systems. The first ap-
proach is through the use of Neuro-Fuzzy architecture and a learning process
toadaptthefuzzysystemparameters.Thesecondapproachisthroughtheuse
of genetic algorithms as an optimization tool for selecting the most suitable
membership functions and rules for the fuzzy system. The author compares
thetwoapproachesandappliesthemtorobotscommunicationinmulti-robot
teams.
In Chap. 8, which is entitled Modelling the Tennessee Eastman Chemi-
cal Process Reactor Using Fuzzy Logic, the authors namely, Alaa F. Sheta,
introduces the challenges associated with modeling nonlinear dynamical sys-
tems. The least square estimation method and the fuzzy method, were used
to solve the modelling problem for the Tennessee Eastman chemical process
reactor.Thedevelopedresultsshowthatfuzzymodelscanefficientlyperform
like the actual chemical reactor and with a high modelling capabilities.
Rio de Janeiro Nadia Nedjah, Ph.D.
March 2005 Luiza de Macedo Mourelle, Ph.D.

Contents
Part I Fuzzy Theory
1 Introducing You to Fuzziness
N. Nedjah, L. de M. Mourelle ..................................... 3
1.1 Introduction ............................................... 3
1.2 Fuzzy Sets................................................. 4
1.2.1 Linguistic Variables and Terms ......................... 6
1.2.2 Operators............................................ 6
1.3 Fuzzy Relation ............................................. 11
1.4 Fuzzy Logic................................................ 11
1.4.1 Fuzzy Logic Connectives............................... 12
1.4.2 Fuzzy Rules and Inference ............................. 12
1.5 Fuzzy Controllers........................................... 13
1.5.1 Operation ........................................... 14
1.6 Summary.................................................. 20
References ...................................................... 20
2 A Qualitative Approach
for Symbolic Data Manipulation
Under Uncertainty
I. Truck, H. Akdag ............................................... 23
2.1 Introduction ............................................... 23
2.2 Symbolic Data Representation ............................... 26
2.2.1 Formulas for Uncertainty Qualitative Theory............. 27
2.2.2 Axiomatic for Qualitative Uncertainty Theory............ 30
2.2.3 Formal Consequences of This Axiomatic ................. 31
2.2.4 Consequences ........................................ 34
2.3 Symbolic Modification ...................................... 35
2.3.1 Definitions........................................... 36
2.3.2 Order Relation ....................................... 38
2.3.3 Finite and Infinite Modifiers ........................... 39
X Contents
2.3.4 Composition ......................................... 40
2.4 Symbolic Combination: A Median Operator.................... 41
2.4.1 Definitions........................................... 42
2.4.2 Expressing the Median ................................ 45
2.5 Conclusion................................................. 48
References ...................................................... 50
3 Adaptation of Fuzzy Inference System
Using Neural Learning
A. Abraham ..................................................... 53
3.1 Introduction ............................................... 53
3.2 Cooperative Neuro-Fuzzy Systems ............................ 54
3.2.1 Fuzzy Associative Memories............................ 54
3.2.2 Fuzzy Rule Extraction Using Self Organizing Maps ....... 55
3.2.3 Systems Capable of Learning Fuzzy Set Parameters ....... 56
3.3 Concurrent Neuro-Fuzzy System.............................. 57
3.4 Integrated Neuro-Fuzzy Systems.............................. 57
3.4.1 Mamdani Integrated Neuro-Fuzzy Systems ............... 58
3.4.2 Takagi-Sugeno Integrated Neuro-Fuzzy System ........... 59
3.4.3 Adaptive Network Based Fuzzy Inference System (ANFIS). 60
3.4.4 Fuzzy Adaptive Learning Control Network (FALCON) .... 62
3.4.5 Generalized Approximate Reasoning
Based Intelligent Control (GARIC) ..................... 63
3.4.6 Neuro-Fuzzy Controller (NEFCON) ..................... 64
3.4.7 Neuro-Fuzzy Classification (NEFCLASS) ................ 65
3.4.8 Neuro-Fuzzy Function Approximation (NEFPROX) ....... 67
3.4.9 Fuzzy Inference Environment Software
with Tuning (FINEST) ................................ 68
3.4.10 Self Constructing Neural Fuzzy
Inference Network (SONFIN) .......................... 69
3.4.11 Fuzzy Net (FUN)..................................... 71
3.4.12 Evolving Fuzzy Neural Networks (EFuNN)............... 73
3.4.13 Dynamic Evolving Fuzzy Neural Networks (dmEFuNNs)... 74
3.5 Discussions ................................................ 75
3.5.1 Evolutionary and Neural Learning
of Fuzzy Inference System (EvoNF) ..................... 77
3.6 Conclusions................................................ 79
3.7 Acknowledgements.......................................... 79
References ...................................................... 80