Null-Additive Set Functions

Null-Additive Set Functions

by Endre Pap
     
 

This volume presents a unified approach to the mathematical theory of a wide class of non-additive set functions, the so called null-additive set functions, which also includes classical measure theory. It includes such important set functions as capacities, triangular set functions, some fuzzy measures, submeasures, decomposable measures, possibility measures,

Overview

This volume presents a unified approach to the mathematical theory of a wide class of non-additive set functions, the so called null-additive set functions, which also includes classical measure theory. It includes such important set functions as capacities, triangular set functions, some fuzzy measures, submeasures, decomposable measures, possibility measures, distorted probabilities, auontinuous set functions, etc.
The usefulness of the theory is demonstrated by applications in nonlinear differential and difference equations; fractal geometry in the theory of chaos; the approximation of functions in modular spaces by nonlinear singular integral operators; and in the theory of diagonal theorems as a universal method for proving general and fundamental theorems in functional analysis and measure theory.
Audience: This book will be of value to researchers and postgraduate students in mathematics, as well as in such diverse fields as knowledge engineering, artificial intelligence, game theory, statistics, economics, sociology and industry.

Editorial Reviews

Booknews
Pap (mathematics, U. of Novi Sad, Yugoslavia) presents a unified approach to the mathematical theory of a wide class of non- additive set functions called null-additive, which also includes classical measure theory. Among the set functions he considers are capacities, triangular set functions, some fuzzy measures, submeasures, decomposable and possibility measures, distorted probabilities, and autocontinuous set functions. He also demonstrates the application of the theory in nonlinear differential and difference equations, the fractal geometry of chaos theory, the approximations of functions in modular spaces by nonlinear singular integral operators, and other contexts. For researchers in mathematics, artificial intelligence, statistics, and related fields. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN-13:
9789048146024
Publisher:
Springer Netherlands
Publication date:
12/10/2010
Series:
Mathematics and Its Applications (closed) Series , #337
Edition description:
Softcover reprint of hardcover 1st ed. 1995
Pages:
315
Product dimensions:
6.30(w) x 9.45(h) x 0.03(d)

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