A note on the superadditive and the subadditive transformations of aggregation functions

TL;DR

This paper explores the mathematical properties of superadditive and subadditive transformations of aggregation functions, providing conditions for their properness and examining their interrelations.

Contribution

It offers a comprehensive theoretical analysis of the transformations, including necessary and sufficient conditions for their properness and their relationships.

Findings

Derived conditions for properness of transformations

Analyzed relationships between superadditive and subadditive transformations

Provided examples illustrating key concepts

Abstract

We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function is again proper are deeply studied and exemplified. Relationships between these transformations are also studied.