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Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions

dc.contributor.authorMarichal, Jean-Luc
dc.contributor.authorCouceiro, Miguel
HAL ID: 1498
dc.date.accessioned2012-09-26T14:12:02Z
dc.date.available2012-09-26T14:12:02Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10235
dc.language.isoenen
dc.subjectAggregation functionen
dc.subjectdiscrete Choquet integralen
dc.subjectLovász extensionen
dc.subjectfunctional equationen
dc.subjectcomonotonic modularityen
dc.subjectinvariance under horizontal differenceen
dc.subjectaxiomatizationen
dc.subject.ddc515en
dc.titleAxiomatizations of quasi-Lovász extensions of pseudo-Boolean functionsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversite du Luxembourg;
dc.description.abstractenWe introduce the concept of quasi-Lovász extension as being a mapping f:InR defined on a nonempty real interval I containing the origin and which can be factorized as f(x 1, . . . , x n ) = L(φ(x 1), . . . , φ(x n )), where L is the Lovász extension of a pseudo-Boolean function :01nR (i.e., the function L:RnR whose restriction to each simplex of the standard triangulation of [0, 1] n is the unique affine function which agrees with ψ at the vertices of this simplex) and :IR is a nondecreasing function vanishing at the origin. These functions appear naturally within the scope of decision making under uncertainty since they subsume overall preference functionals associated with discrete Choquet integrals whose variables are transformed by a given utility function. To axiomatize the class of quasi-Lovász extensions, we propose generalizations of properties used to characterize Lovász extensions, including a comonotonic version of modularity and a natural relaxation of homogeneity. A variant of the latter property enables us to axiomatize also the class of symmetric quasi-Lovász extensions, which are compositions of symmetric Lovász extensions with 1-place non decreasing odd functions.en
dc.relation.isversionofjnlnameAequationes Mathematicae
dc.relation.isversionofjnlvol82en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages213-231en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00010-011-0091-0en
dc.identifier.urlsitehttp://arxiv.org/abs/1011.6302en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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