Generalized Measure Theory

2009
ISBN: 978-0-387-76851-9
Verlag: Springer US

Buch, Englisch, Band 25, 384 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 764 g

Reihe: IFSR International Series in Systems Science and Systems Engineering

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.

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.