Axiomatizations of signed discrete Choquet integrals

TL;DR

This paper provides axiomatizations of the signed discrete Choquet integral, a non-monotonic extension of the classical integral, using functional equations and conditions that highlight its properties in aggregation theory.

Contribution

It introduces new axiomatizations for the signed discrete Choquet integral, expanding the theoretical framework of aggregation functions.

Findings

Axiomatizations via functional equations

Necessary and sufficient conditions identified

Enhanced understanding of non-monotonic integrals

Abstract

We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lov\'asz extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable properties in aggregation theory.