Generalized Measure Theory

1. Front Matter

   Pages i-xv

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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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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.

• choquet integral
• integral
• integration
• mathematical analysis
• measure
• measure theory

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)

• 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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