FUZZY MEASURES AND FUZZY INTEGRALS: AN OVERVIEW

Abstract

This paper provides an overview of fuzzy measures, fuzzy integration theories and Choquet's capacity theory. Belief, plausibility, and possibility measures are characterized as Choquet capacities and as fuzzy measures. The relationship between possibility measures, fuzzy sets, and approximate reasoning is established. Recent results on extensions of fuzzy measures, structural characteristics of fuzzy measures, and convergence of function sequences on fuzzy measure spaces are presented. Fuzzy measure integration concepts due to Sugeno and Choquet and their applications are discussed. An extensive list of references to the literature of fuzzy measures, Sugeno and Choquet integrals, fuzzy probabilities, fuzzy random variables, probabilistic sets, and random sets is provided. Applicalions discussed or referenced include information fusion, information retrieval, approximate reasoning, artificial intelligence, uncertainty theory, and control and decision theory.

INDEX TERMS:

• Choquet capacity
• Choquet integral
• Dempster-Shafer theory
• fuzzy integral
• fuzzy measure
• Sugeno integral
• possibility theory
• probabilistic set
• random set
• uncertainty

Additional information

Notes on contributors

WANG ZHENYUAN

Professor Wang is currently on leave from the Department of Mathematics, Hebei University, People's Republic of China.