Mathematics of Fuzziness – Basic Issues

Xuzhu Wang, Da Ruan, Etienne E. Kerre (auth.)3540783105, 9783540783107

Mathematics of Fuzziness—Basic Issues introduces a basic notion of ‘fuzziness’ and provides a conceptual mathematical framework to characterize such fuzzy phenomena in 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.

Table of contents :
Front Matter….Pages –
Preliminaries….Pages 1-20
Basics of Fuzzy Sets….Pages 21-64
Fuzzy Relations….Pages 65-111
Extension Principle and Fuzzy Numbers….Pages 113-151
A Brief Introduction to Some Pure Mathematical Topics….Pages 153-188
Fuzzy Inference and Fuzzy Control….Pages 189-205
Back Matter….Pages –