MONOTONE SET-FUNCTIONS DEFINED BY CHOQUET INTEGRAL

Given a nonnegative monotone set function and a nonnegative measurable function on a measurable space, the Choquet integral determines a new nonnegative monotone set function that is absolutely continuous with respect to the original one (in a generalized sense for monotone set f unctions). This new set function preserves almost all desirable struct ural characteristics of the original monotone set function, such as co ntinuity, subadditivity, superadditivity, null-additivity, converse-nu ll-additivity, autocontinuity, converse-autocontinuity, uniform autoco ntinuity, uniform converse-autocontinuity, and fuzzy multiplicativity. Such a construction is a useful method to define sound fuzzy measures in various applications.