Mathematics of Fuzziness – Basic Issues [electronic resource] / by Xuzhu Wang, Da Ruan, Etienne E. Kerre.Material type: TextLanguage: English Series: Studies in Fuzziness and Soft Computing: 245Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: XII, 220 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540783114Subject(s): Engineering | Artificial intelligence | Mathematics | Engineering mathematics | Engineering | Appl.Mathematics/Computational Methods of Engineering | Artificial Intelligence (incl. Robotics) | Applications of MathematicsAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: TA329-348TA640-643Online resources: Click here to access online
Preliminaries -- Basics of Fuzzy Sets -- Fuzzy Relations -- Extension Principle and Fuzzy Numbers -- A Brief Introduction to Some Pure Mathematical Topics -- Fuzzy Inference and Fuzzy Control.
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.