【摘 要】
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Structural characteristics and absolute continuities of monotone set-valued function defined by set-valued Choquet integral are discussed. Similar to the single
【机 构】
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School of Management and Economics
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Structural characteristics and absolute continuities of monotone set-valued function defined by set-valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structural characteristics of set-valued function are defined and have been proven the same as those in the original set functions, such as null-additivity, weakly null-additivity, order continuity, strong order continuity and property(S). A counterexample shows that order continuity and strong order continuity of the original set functions are no longer kept in a monotone set-valued function when Choquet integrably bounded assumption is abandoned. Four kinds of absolute continuities are defined for set-valued function, and all been proven valid with respect to the original set functions.
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