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Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others.
Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction.
This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request.
List of contents
1 Introduction to Fuzzy Sets.- 2 Fuzzy Sets-Basic Definitions.- 3 Extensions.- 4 Fuzzy Measures and Measures of Fuzziness.- 5 The Extension Principle and Applications.- 6 Fuzzy Relations and Fuzzy Graphs.- 7 Fuzzy Analysis.- 8 Possibility Theory, Probability Theory, and Fuzzy Set.- 9 Fuzzy Logic and Approximate Reasoning.- 10 Expert Systems and Fuzzy Control.- 11 Pattern Recognition.- 12 Decision Making in Fuzzy Environments.- 13 Fuzzy Set Models in Operations Research.- 14 Empirical Research in Fuzzy Set Theory.- 15 Future Perspectives.
About the author
Prof. em. Dr. Drs. h. c. Hans-Jürgen Zimmermann war bis 1999 Inhaber des Lehrstuhls für Unternehmensforschung (Operations Research) an der RWTH Aachen und ist Wissenschaftlicher Leiter der ELITE (European Laboratory for Intelligent Techniques Engineering) sowie wissenschaftlicher Beirat des Instituts für Operations Research und Management, Inform GmbH, in Aachen.
Report
`... Professor Zimmermann's treatise is a major contribution to the literature of fuzzy sets and decision analysis. '
L.A. Zadeh from the Foreword
`I highly recommend this text for students, both novice and advanced in theory and applications, academics and industrial researchers. Of course, this book is a must for all academic libraries. Indeed, Professor Zimmermann, who as a researcher, author, editor and organizer of international meetings has contributed so much for the cause of the fuzzy sets and systems and the fuzzy community, deserves our compliments.'
Madan M. Gupta, Intelligent Systems Research Laboratory, University of Saskatchewan, Canada
`...the extensive bibliography, as well as the excellent chapters on applications are of wide interest. Those teaching courses in fuzzy set theory, especially in a more practical rather than abstract context, would do well to consider this textbook. Zimmermann has compiled a collection of information that is useful, clearly presented, and with the latest revision, reflects much current research.'
International Journal of General Systems, 21 (1992)
`The up-to-date content as well as the author's style and method of presentation make the book to be one of the best presentations of the whole field of fuzziness and will maintain its role as one of the preferred introductions into that topic.'
European Journal of Operations Research
