Lifting continuity properties of aggregation functions to their super- and sub-additive transformations

We investigate possible extensions of various types of continuity of aggregation functionsto their super- and sub-additive transformations. More speci cally, we examine liftsof classical, uniform, Lipschitz and Holder continuities and di erentiability. The classical,uniform, and Lipschitz continuities turn out to be preserved by super- and sub-additivetransformations (albeit for uniform continuity and the super-additive case we prove itonly in dimension one), while the Holder continuity and di erentiability are not.

Keywords:

aggregation function , super- and sub-additive transformations , continuity