Regular fuzzy measure and representation of comonotonically additive functional

This paper discusses the functional I defined on the class of continuous fu nctions, which is comonotonically additive and monotone. The notion of regu lar fuzzy measure is proposed and the uniqueness theorem of regular fuzzy m easure is shown, it is also shown that I can be represented by the differen ce of two Choquet integrals with respect to regular fuzzy measures when the universal set X is a locally compact Hausdorff space, and that I can be re presented by one Choquet integral with respect to a regular fuzzy measure w hen X is a compact Hausdorff space. (C) 2000 Elsevier Science B.V. All righ ts reserved.