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dc.contributor.authorMarichal, Jean-Luc
dc.contributor.authorCouceiro, Miguel
HAL ID: 1498
dc.date.accessioned2012-09-27T09:34:25Z
dc.date.available2012-09-27T09:34:25Z
dc.date.issued2012-09-27
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10258
dc.language.isoenen
dc.subjectFunctional equationen
dc.subjectLovász extensionen
dc.subjectDiscrete symmetric Choquet integralen
dc.subjectDiscrete Choquet integralen
dc.subjectAggregation functionen
dc.subject.ddc3en
dc.titleAxiomatizations of Lovász extensions of pseudo-Boolean functionsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversité du Luxembourg;Luxembourg
dc.description.abstractenThree important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity conditions, these functions coincide with the Lovász extensions vanishing at the origin, which subsume the discrete Choquet integrals. We also propose a simultaneous generalization of horizontal min-additivity and horizontal max-additivity, called horizontal median-additivity, and we describe the corresponding function class. Additional conditions then reduce this class to that of symmetric Lovász extensions, which includes the discrete symmetric Choquet integrals.en
dc.relation.isversionofjnlnameFuzzy Sets and Systems
dc.relation.isversionofjnlvol181en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2011-10
dc.relation.isversionofjnlpages28–38en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.fss.2011.05.006en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelRecherche opérationnelleen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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