A theory of fuzzy measures: Representations, the Choquet integral, and null sets. (English) Zbl 0735.28015

Murofushi, Toshiaki; Sugeno, Michio

J. Math. Anal. Appl. 159, No. 2, 532-549 (1991).

Regardless the continuity, authors define the fuzzy measure as a nonnegative monotone set function on a measurable space. By using classical measures, a representation of fuzzy measures is shown in this paper. Furthermore, the authors give a necessary and sufficient condition that, for any given fuzzy measure, the Choquet integral is additive. Also, the authors generalize the concepts of null sets and ”a.e.” on fuzzy measure spaces.

Reviewer: Wang Zhenyuan (Binghamton)

MSC:

28E10

Fuzzy measure theory

Keywords:

representation; fuzzy measures; Choquet integral; null set

References:

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