<EM>Mathematics of Fuzziness—Basic Issues introduces a basic notion of ‘fuzziness’ and provides a conceptual mathematical framework to characterize such fuzzy phenomena in <EM>Studies in Fuzziness and Soft Computing. The book systematically presents a self-contained introduction to the essentials of mathematics of fuzziness ranging from fuzzy sets, fuzzy relations, fuzzy numbers, fuzzy algebra, fuzzy measures, fuzzy integrals, and fuzzy topology to fuzzy control in a strictly mathematical manner. It contains most of the authors’ research results in the field of fuzzy set theory and has evolved from the authors’ lecture notes to both undergraduate and graduate students over the last three decades. A lot of exercises in each chapter of the book are particularly suitable as a textbook for any undergraduate and graduate student in mathematics, computer science and engineering. The reading of the book will surely lay a solid foundation for further research on fuzzy set theory and its applications.
Xuzhu Wang, Da Ruan and Etienne E. Kerre Mathematics of Fuzziness – Basic Issues
Studies in Fuzziness and Soft Computing, Volume 245 Editor-in-Chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail:
[email protected] Further volumes of this series can be found on our homepage: springer.com Vol. 228. Adam Kasperski Discrete Optimization with Interval Data, 2008 ISBN 978-3-540-78483-8 Vol. 230. Bhanu Prasad (Ed.) Soft Computing Applications in Business, 2008 ISBN 978-3-540-79004-4 Vol. 231. Michal Baczynski, Balasubramaniam Jayaram Soft Fuzzy Implications, 2008 ISBN 978-3-540-69080-1 Vol. 232. Eduardo Massad, Neli Regina Siqueira Ortega, Laécio Carvalho de Barros, Claudio José Struchiner Fuzzy Logic in Action: Applications in Epidemiology and Beyond, 2008 ISBN 978-3-540-69092-4 Vol. 233. Cengiz Kahraman (Ed.) Fuzzy Engineering Economics with Applications, 2008 ISBN 978-3-540-70809-4 Vol. 234. Eyal Kolman, Michael Margaliot Knowledge-Based Neurocomputing: A Fuzzy Logic Approach, 2009 ISBN 978-3-540-88076-9 Vol. 235. Kofi Kissi Dompere Fuzzy Rationality, 2009 ISBN 978-3-540-88082-0 Vol. 236. Kofi Kissi Dompere Epistemic Foundations of Fuzziness, 2009 ISBN 978-3-540-88084-4
Vol. 237. Kofi Kissi Dompere Fuzziness and Approximate Reasoning, 2009 ISBN 978-3-540-88086-8 Vol. 238. Atanu Sengupta, Tapan Kumar Pal Fuzzy Preference Ordering of Interval Numbers in Decision Problems, 2009 ISBN 978-3-540-89914-3 Vol. 239. Baoding Liu Theory and Practice of Uncertain Programming, 2009 ISBN 978-3-540-89483-4 Vol. 240. Asli Celikyilmaz, I. Burhan Türksen Modeling Uncertainty with Fuzzy Logic, 2009 ISBN 978-3-540-89923-5 Vol. 241. Jacek Kluska Analytical Methods in Fuzzy Modeling and Control, 2009 ISBN 978-3-540-89926-6 Vol. 242. Yaochu Jin, Lipo Wang Fuzzy Systems in Bioinformatics and Computational Biology, 2009 ISBN 978-3-540-89967-9 Vol. 243. Rudolf Seising (Ed.) Views on Fuzzy Sets and Systems from Different Perspectives, 2009 ISBN 978-3-540-93801-9 Vol. 244. Xiaodong Liu and Witold Pedrycz Axiomatic Fuzzy Set Theory and Its Applications, 2009 ISBN 978-3-642-00401-8 Vol. 245. Xuzhu Wang, Da Ruan, Etienne E. Kerre Mathematics of Fuzziness – Basic Issues, 2009 ISBN 978-3-540-78310-7
Xuzhu Wang, Da Ruan and Etienne E. Kerre
Mathematics of Fuzziness – Basic Issues
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Authors Prof. Dr. Da Ruan Belgian Nuclear Research Centre (SCK • CEN) Boeretang 200 2400 Mol Belgium E-mail:
[email protected]
Prof. Dr. Xuzhu Wang Department of Mathematics Taiyuan Universi