Complexity Management in Fuzzy Systems

1. Front Matter

   Pages I-XV

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2. Introduction

   • Alexander Gegov

   Pages 1-6

3. Basic Types of Fuzzy Rule Based Systems

   • Alexander Gegov

   Pages 7-16

4. Rule Base Reduction Methods for Fuzzy Systems

   • Alexander Gegov

   Pages 17-31

5. Formal Presentation of Fuzzy Rule Based Systems

   • Alexander Gegov

   Pages 33-63

6. Formal Manipulation of Fuzzy Rule Based Systems

   • Alexander Gegov

   Pages 65-114

7. Formal Manipulation with Special Rule Bases

   • Alexander Gegov

   Pages 115-151

8. Formal Transformation of Fuzzy Rule Based Systems

   • Alexander Gegov

   Pages 153-183

9. Formal Transformation of Feedback Rule Bases

   • Alexander Gegov

   Pages 185-268

10. Formal Simplification of Fuzzy Rule Based Systems

    • Alexander Gegov

    Pages 269-340

11. Conclusion

    • Alexander Gegov

    Pages 341-344

12. Back Matter

    Pages 345-351

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Doing research is a great adventure As any adventure sometimes it is hard You may feel alone and with no idea where to go But if you have courage and press onwards You will eventually stand where no one has stood And see the world as no one has seen it There can be no better feeling than this! Adaptation from ‘Introduction to Research’, Tom Addis (2004) The idea about this book has been on the author’s mind for almost a decade but it was only about a couple of years ago when the underlying research process was actually started. The reason for this delay has been the insufficient spare time for research being a lecturer in a ‘new’ UK university where the emphasis is mainly on teaching. And maybe this book would have never been written if the author had not been presented with the chance of developing new teaching modules in fuzzy logic that have given him food for thought in a research related context and have helped him combine efficiently his teaching and research activities. The title of this book may sound too specialised but it has a much wider meaning. Fuzzy systems are any systems for modelling, simulation, control, prediction, diagnosis, decision making, pattern recognition, image processing, etc. which use fuzzy logic. Although fuzzy logic is an advanced extension of binary logic, the latter is still used predominantly today.

• Complex fuzzy systems
• Computer-Aided Design (CAD)
• Fuzzy
• Fuzzy rule aggregation
• Fuzzy rule base compression
• Fuzzy rule base reduction
• Fuzzy rule filtration
• Transformation
• algorithm
• algorithms
• complexity
• formal method
• fuzzy system
• fuzzy systems
• multi-agent system

From the reviews:

“Prof. Gegov’s book is a timely contribution to a very rapidly evolving field––as he terms it, the field of complexity management. … book would be an important addition to the library of anyone doing serious work in the development of fuzzy systems. … This book will help many serious practitioners make fuzzy systems a more compact and efficient modeling approach to deal with complex systems which are described by a large number of rules.” (Timothy J. Ross, Artificial Intelligence, Vol. 171 (18), 2007)

“The book is presented in such a way that it could be very useful for both academic and industrial researchers as a research monograph to advance their knowledge in fuzzy systems. It could also be used to some extend as a text book for both undergraduate and postgraduate studies interested in fuzzy systems. … book is written in a lucid and reader-friendly style supported by many examples and line diagrams illustration. … This well presented and written book admirably meets the goals of its author.” (Ahmad Lotfi, Journal of Multiple-Valued Logic and Soft Computing, Vol. 15, 2008)

“If you have … wish to take fuzzy logic ideas further and place them on a firm theoretical foundation, then this book may be for you. … In conclusion, this book is a useful addition for specialists interested in the theoretical and mathematical underpinnings of fuzzy systems.” (Adrian A. Hopgood, International Journal of Hybrid Intelligent Systems, Vol. 5, 2008)

“This approach is different from the mainstream approach of complexity reduction in fuzzy systems … . author presents the subject with enthusiasm, greatinterest and mastering of the subject. … The book is considered a major contribution to both the qualitative and quantitative aspects of complexity in fuzzy based systems. … author has succeeded in using both qualitative and quantitative approaches of representation in order to manage complexity. Therefore, he should be congratulated for his contribution to the field of managing complexity in fuzzy systems.” (Ashraf Labib, Fuzzy Sets and Systems, Vol. 161 (21), November, 2010)

“The book presents a novel systematic methodology for the qualitative analysis of rule bases and provides methods and algorithms to manipulate and simplify them. … On the other hand, given the novelty of the techniques presented, one can imagine that such examples are not readily available. In that sense, the book is likely to attract more readers from the academia than researchers in industry or practicing engineers.” (Robert Babuška, IEEE Computational Intelligence Magazine, November, 2007)

• School of Computing Buckingham Building, University of Portsmouth, Portsmouth, United Kingdom

  Alexander Gegov

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