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Sims, John R.; Wang, Zhenyuan

Fuzzy measures and fuzzy integrals: An overview. (English) Zbl 0699.28010

Int. J. Gen. Syst. 17, No. 2-3, 157-189 (1990).
Summary: 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. Applications discussed or referenced include information fusion, information retrieval, approximate reasoning, artificial intelligence, uncertainty theory, and control and decision theory.

Cited in 7 Documents

MSC:

28E10 Fuzzy measure theory

Keywords:

Dempster-Shafer theory; Sugeno integral; fuzzy measures; fuzzy integration; possibility measures; Choquet capacities; fuzzy sets; approximate reasoning; Choquet integrals; probabilistic sets; random sets; information fusion; information retrieval; artificial intelligence; uncertainty theory; control; decision theory
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