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dc.contributor.authorMarichal, Jean-Luc
dc.contributor.authorCouceiro, Miguel
HAL ID: 1498
dc.date.accessioned2012-09-27T11:41:25Z
dc.date.available2012-09-27T11:41:25Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10267
dc.language.isoenen
dc.subjecthorizontal additivityen
dc.subjectcomonotonic additivityen
dc.subjectCauchy equationen
dc.subjectfunctional equationen
dc.subjectLovász extensionen
dc.subjectiscrete symmetric Choquet integralen
dc.subjectdiscrete Choquet integralen
dc.subjectAggregation functionen
dc.subject.ddc003en
dc.titleAxiomatizations of the discrete Choquet integral and extensionsen
dc.typeCommunication / Conférence
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, the latter 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 medianadditivity, 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.ispartoftitleProceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) et les rencontres francophones sur la Logique Floue et ses Applications (LFA-2011), Aix-les-Bains, France, July 18-22, 2011.en
dc.relation.ispartofeditorMauris, G.
dc.relation.ispartofeditorMontero, J.
dc.relation.ispartofeditorGalichet, S.
dc.relation.ispartofpublnameEuropean Society for Fuzzy Logic and Technologyen
dc.relation.ispartofdate2011
dc.relation.ispartofpages1097 p.en
dc.subject.ddclabelRecherche opérationnelleen
dc.relation.ispartofisbn978-90-78677-00-0en
dc.relation.conftitleEUSFLAT/LFA 2011en
dc.relation.confdate2011-07
dc.relation.confcityAix les Bainsen
dc.relation.confcountryFranceen
dc.relation.forthcomingnonen


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