Some characterizations of a mapping defined by interval-valued Choquet integrals

Abstract

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings <TEX>${\phi}$</TEX> on the class of Choquet integrable functions and m-convex mappings <TEX>$T_{\phi}$</TEX>, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.