Transformations of aggregation functions: Local versus global properties and approximation

Abstract

Aggregation functions have been extensively studied from numerous points of view, driven by both theoretical interest as well as real-world applications. We will focus on transformations of aggregation functions, and on super- and sub-additive transformations in particular. Global properties of such transformations may depend on local behaviour of the input aggregation functions and we will look at this phenomenon more closely. We will conclude with addressing approximation of transformations and discuss applications of aggregation functions in discrete structures.