SUPER- an‎d SUB-ADDITIVE ENVELOPES OF AGGREGATION FUNCTIONS: INTERPLAY BETWEEN LOCAL an‎d GLOBAL PROPERTIES, an‎d APPROXIMATION

Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and Sipeky [The superadditive and the subadditive transformations of integrals and aggrega- tion functions, Fuzzy Sets and Systems 291 (2016), 40{53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with a preassigned super- and sub-additive transformation, and ad- dress approximation of these transformations. The underpinning feature of the presented results is dependence of global properties of super- and sub-additive transformations on local properties of aggregation functions.