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Mathematics of Fuzziness—Basic Issues

  • Book
  • © 2009
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Overview

Authors:
  1. Xuzhu Wang

    1. Taiyuan University of Technology, China

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  2. Da Ruan

    1. Belgian Nuclear Research Centre and Ghent University, Belgium

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  3. Etienne E. Kerre

    1. Ghent University, Belgium

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  • Systematic, self-contained introduction to the essentials of mathematics of fuzziness
  • Contains a lot of exercises in each section

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 245)

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Table of contents (6 chapters)

  1. Front Matter

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  2. Preliminaries

    • Xuzhu Wang, Da Ruan, Etienne E. Kerre
    Pages 1-20
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  3. Basics of Fuzzy Sets

    • Xuzhu Wang, Da Ruan, Etienne E. Kerre
    Pages 21-64
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  4. Fuzzy Relations

    • Xuzhu Wang, Da Ruan, Etienne E. Kerre
    Pages 65-111
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  5. Extension Principle and Fuzzy Numbers

    • Xuzhu Wang, Da Ruan, Etienne E. Kerre
    Pages 113-151
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  6. A Brief Introduction to Some Pure Mathematical Topics

    • Xuzhu Wang, Da Ruan, Etienne E. Kerre
    Pages 153-188
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  7. Fuzzy Inference and Fuzzy Control

    • Xuzhu Wang, Da Ruan, Etienne E. Kerre
    Pages 189-205
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  8. Back Matter

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Keywords

About this book

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.

Reviews

From the reviews: “Aptly titled, it is an interesting undergraduate course resource for those who are just getting their feet wet in the study of fuzziness. … All basic concepts are duly presented … . authors manage to marry two things that other textbooks fail to: extensive coverage of topics in only 200 pages in combination with a wealth of end-of-chapter exercises. … reviewer wishes that this volume was available when he was an undergrad! Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and general readers.” (G. Trajkovski, Choice, Vol. 47 (3), November, 2009)

Authors and Affiliations

  • Taiyuan University of Technology, China

    Xuzhu Wang

  • Belgian Nuclear Research Centre and Ghent University, Belgium

    Da Ruan

  • Ghent University, Belgium

    Etienne E. Kerre

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