A theory of fuzzy measures: Representations, the Choquet integral, and null sets (Q1176588)

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.