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

AbstractSome theorems of T. Murofushi and M. Sugeno (Fuzzy Sets and Systems 29 (1989), 201–227) concerning representation of fuzzy measures and the Choquet integral are generalized. It is shown that, if there is a certain relation between two measurable functions, then the Choquet integral is additive for these two functions. In addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a σ-algebra