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.


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