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

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.

### MSC:

 2.8e+11 Fuzzy measure theory

### Keywords:

representation; fuzzy measures; Choquet integral; null set
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### References:

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