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Choquet integral and fuzzy measures on locally compact space. (English) Zbl 0977.28012

Summary: The concept of outer regular fuzzy measures is proposed, and it is shown that a functional of certain type on the cone of positive continuous functions with compact supports is represented as a Choquet integral with respect to an outer regular fuzzy measure. It is also shown that the Choquet integral of positive continuous functions with compact supports is represented as a Lebesgue integral with the same integrands. This representation is a generalization of certain previous results of others, which are useful for computation of the upper and lower expected value.

MSC:

28E10 Fuzzy measure theory
28C99 Set functions and measures on spaces with additional structure
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