Axiomatizations of signed discrete Choquet integrals
Giove, Silvio; Marichal, Jean-Luc; Cardin, Marta; Couceiro, Miguel (2011), Axiomatizations of signed discrete Choquet integrals, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 19, 2, p. 193-200. http://dx.doi.org/10.1142/S0218488511006964
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1007.0711
Journal nameInternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
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Abstract (EN)We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász 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.
Subjects / KeywordsSigned discrete Choquet integral; signed capacity; Lovász extension; functional equation; comonotonic additivity; homogeneity; axiomatization
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