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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

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1007.0711
Date
2011
Journal name
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Volume
19
Number
2
Publisher
World Scientific
Pages
193-200
Publication identifier
Metadata
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Author(s)
Giove, Silvio
Marichal, Jean-Luc
Cardin, Marta
Couceiro, Miguel
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 / Keywords
Signed discrete Choquet integral; signed capacity; Lovász extension; functional equation; comonotonic additivity; homogeneity; axiomatization