The comonotonically additive functional on the class of continuous functions with compact support

This paper discusses the functional I defined on the class of continuous functions K, which is comonotonically additive and monotone. It is shown that the functional I can be represented by the difference of two Choquet integrals with respect to regular fuzzy measures when the universal set X is a locally compact Hausdorff space, and that the functional I can be represented by one Choquet integral with respect to a regular fuzzy measure when X is a compact Hausdorff space.