We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovasz 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.
Axiomatizations of signed discrete Choquet integrals
CARDIN, Marta;GIOVE, Silvio;
2011-01-01
Abstract
We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovasz 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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