Generalized Measure Theory

1. Auflage. Softcover version of original hardcover Auflage 2009
ISBN: 978-1-4419-4576-1
Verlag: Springer US

Buch, Englisch, Band 25, 384 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 604 g

Reihe: IFSR International Series in Systems Science and Systems Engineering

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.

Zielgruppe

Research

Autoren/Hrsg.

Klir, George J.

Wang, Zhenyuan

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

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.