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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.accessioned2021-10-14T08:54:15Z
dc.date.available2021-10-14T08:54:15Z
dc.date.issued2020
dc.identifier.issn0022-2496
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22000
dc.language.isoenen
dc.subjectSemiorderen
dc.subjectNumerical representationen
dc.subjectConstant thresholden
dc.subjectCountable setsen
dc.subject.ddc519en
dc.titleUnit representation of semiorders I: Countable setsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper proposes a new proof of the existence of constant threshold representations of semiorders on countably infinite sets. The construction treats each indifference-connected component of the semiorder separately. It uses a partition of such an indifference-connected component into indifference classes. Each element in the indifference-connected component is mirrored, using a “ghost” element, into a reference indifference class that is weakly ordered. A numerical representation of this weak order is used as the basis for the construction of the unit representation after an appropriate lifting operation. We apply the procedure to each indifference-connected component and assemble them adequately to obtain an overall unit representation.Our proof technique has several original features. It uses elementary tools and can be seen as the extension of a technique designed for the finite case, using a denumerable set of inductions. Moreover, it gives us much control on the representation that is built, so that it is, for example, easy to investigate its uniqueness. Finally, we show in a companion paper that our technique can be extended to the general (uncountable) case, almost without changes, through the addition of adequate order-denseness conditions.en
dc.relation.isversionofjnlnameJournal of Mathematical Psychology
dc.relation.isversionofjnlvol103en
dc.relation.isversionofjnlissue102566en
dc.relation.isversionofjnldate2021-08
dc.relation.isversionofdoi10.1016/j.jmp.2021.102566en
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.updated2021-10-14T08:50:23Z
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