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Generalized Measure Theory

  • Textbook
  • © 2009

Overview

Authors:
  1. Zhenyuan Wang

    1. Department of Mathematics, University of Nebraska at Omaha, Omaha, U.S.A.

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  2. George J. Klir

    1. Thomas J. Watson School of Engineering, Department of Systems Science &, Binghamton University, Binghamton, U.S.A.

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    You can also search for this author in PubMed   Google Scholar

  • Most up-to-date textbook in the field, covering recent applications
  • Numerous examples motivate the theory and exercises at the end of the chapter provide practice to the student
  • Useful to an interdisciplinary cadre of mathematicians, engineers, computer scientists and specialists working in decision making
  • Includes supplementary material: sn.pub/extras

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction

    • Zhenyuan Wang, George J. Klir
    Pages 1-8

  3. Preliminaries

    • Zhenyuan Wang, George J. Klir
    Pages 9-60

  4. Basic Ideas of Generalized Measure Theory

    • Zhenyuan Wang, George J. Klir
    Pages 61-72

  5. Special Areas of Generalized Measure Theory

    • Zhenyuan Wang, George J. Klir
    Pages 73-103

  6. Extensions

    • Zhenyuan Wang, George J. Klir
    Pages 111-132

  7. Structural Characteristics for Set Functions

    • Zhenyuan Wang, George J. Klir
    Pages 133-150

  8. Measurable Functions on Monotone Measure Spaces

    • Zhenyuan Wang, George J. Klir
    Pages 151-165

  9. Integration

    • Zhenyuan Wang, George J. Klir
    Pages 167-178

  10. Sugeno Integrals

    • Zhenyuan Wang, George J. Klir
    Pages 179-211

  11. Pan-Integrals

    • Zhenyuan Wang, George J. Klir
    Pages 213-223

  12. Choquet Integrals

    • Zhenyuan Wang, George J. Klir
    Pages 225-246

  13. Upper and Lower Integrals

    • Zhenyuan Wang, George J. Klir
    Pages 247-274

  14. Constructing General Measures

    • Zhenyuan Wang, George J. Klir
    Pages 275-284

  15. Fuzzification of Generalized Measures and the Choquet Integral

    • Zhenyuan Wang, George J. Klir
    Pages 285-302

  16. Applications of Generalized Measure Theory

    • Zhenyuan Wang, George J. Klir
    Pages 303-342

  17. Back Matter

    Pages 343-381
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Keywords

About this book

In 1992 we published a book entitled Fuzzy Measure Theory (Plenum Press, New York), in which the term ‘‘fuzzy measure’’ was used for set functions obtained by replacing the additivity requirement of classical measures with weaker requirements of monotonicity with respect to set inclusion and con- nuity. That is, the book dealt with nonnegative set functions that were mo- tone, vanished at the empty set, and possessed appropriate continuity properties when defined on infinite sets. It seems that Fuzzy Measure Theory was the only book available on the market at that time devoted to this emerging new mathematical theory. Some ten years after its publication we began to see that the subject had expanded so much that a second edition of the book, or even a new book on the subject, was needed. We eventually decided to write a new book because the new material we wished to include was too extensive for—and far beyond the usual scope—of a second edition. More importantly, we felt that some fundamental changes regarding this topic’s scope and terminology would be desirable and timely.

Reviews

From the reviews:

“The monograph contains many original results of the authors and provides an excellent introduction to the emerging field of generalized measure theory. The presentation of the large material is given with didactical skill, numerous examples serve for motivation and illustration of results. … easy to read by everyone with a solid background in mathematical analysis, and on this basis in particular for students in mathematics and engineering at the graduate level. … this book can serve as a starting point for research in this area.” (Jan Stankiewicz, Zentralblatt MATH, Vol. 1184, 2010)

Authors and Affiliations

  • Department of Mathematics, University of Nebraska at Omaha, Omaha, U.S.A.

    Zhenyuan Wang

  • Thomas J. Watson School of Engineering, Department of Systems Science &, Binghamton University, Binghamton, U.S.A.

    George J. Klir

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