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

Document Type: Research Paper

Author

Slovak University of Technology in Bratislava, Faculty of Civil Engineer- ing, Department of Mathematics and Descriptive geometry,, Radlinskeho 11, 810 05 Bratislava, Slovakia

Abstract

Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and \v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {\it Fuzzy Sets and Systems} {\bf 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 address 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.

Keywords

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