LIFTING CONTINUITY PROPERTIES OF AGGREGATION FUNCTIONS TO THEIR SUPER- AND SUB-ADDITIVE TRANSFORMATIONS

We investigate possible extensions of various types of continuity of aggregation functions to their super- and sub-additive transformations. More specifically, we examine lifts of classical, uniform, Lipschitz and Holder continuities and differentiability. The classical, uniform, and Lipschitz continuities turn out to be preserved by super- and sub-additive transformations (albeit for uniform continuity and the super-additive case we prove it only in dimension one), while the Holder continuity and differentiability are not.