Axiomatizations of signed discrete Choquet integrals

Details Axiomatizations of signed discrete Choquet integrals Axiomatizations of signed discrete Choquet integrals

2010-07-05

arxiv.org/abs/1007.0711v2

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19 (2) (2011) 193-199

Mathematics

Functional Analysis

Scientific paper

10.1142/S0218488511006964

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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