Axiomatizations of signed discrete Choquet integrals
Marta Cardin, Miguel Couceiro, Silvio Giove, Jean-Luc Marichal

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.
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