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hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorBouyssou, Denis
dc.contributor.authorPirlot, Marc
dc.date.accessioned2021-10-14T08:46:33Z
dc.date.available2021-10-14T08:46:33Z
dc.date.issued2020
dc.identifier.issn0022-2496
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/21999
dc.language.isoenen
dc.subjectsemiorderen
dc.subjectnumerical representationen
dc.subjectconstant thresholden
dc.subjectuncountablesetsen
dc.subject.ddc519en
dc.titleUnit representation of semiorders II: The general caseen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenNecessary and sufficient conditions under which semiorders on uncountable sets can be represented by a real-valued function and a constant threshold are known. We show that the proof strategy that we used for constructing representations in the case of denumerable semiorders can be adapted to the uncountable case. We use it to give an alternative proof of the existence of strict unit representations. In contrast to the countable case, semiorders on uncountable sets that admit a strict unit representation do not necessarily admit a nonstrict unit representation, and conversely. By adapting the proof strategy used for strict unit representations, we establish a characterization of the semiorders that admit a nonstrict representation. Conditions for the existence of other special unit representations are also obtained.en
dc.relation.isversionofjnlnameJournal of Mathematical Psychology
dc.relation.isversionofjnlvol103en
dc.relation.isversionofjnlissue102568en
dc.relation.isversionofjnldate2021-08
dc.relation.isversionofdoi10.1016/j.jmp.2021.102568en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-10-14T08:43:04Z
hal.author.functionaut
hal.author.functionaut


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