Zhenyuan Wang, George J. Klir

Generalized Measure Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

This textbook provides an exhaustive review of generalized measures, from the theoretical background to the latest applications. It is designed as a main text for graduate courses on Generalized Measure Theory, Fuzzy Measure Theory, Theory of Nonadditive Measures and Theory of Monotone Measures. It can also be used as a reference in courses on Fuzzy Sets, Fuzzy Control and Fuzzy Logic.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 384
• Erscheinungstermin: 7. Juli 2010
• Englisch
• ISBN-13: 9780387768526
• Artikelnr.: 43787072

Inhaltsangabe

Preliminaries.- Basic Ideas of Generalized Measure Theory.- Special Areas of Generalized Measure Theory.- Extensions.- Structural Characteristics for Set Functions.- Measurable Functions on Monotone Measure Spaces.- Integration.- Sugeno Integrals.- Pan-Integrals.- Choquet Integrals.- Upper and Lower Integrals.- Constructing General Measures.- Fuzzification of Generalized Measures and the Choquet Integral.- Applications of Generalized Measure Theory.

Rezensionen

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)