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Chain Representations of Nested Families of Biorders

hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorBouyssou, Denis
HAL ID: 182535
ORCID: 0000-0003-3487-8498
hal.structure.identifierDépartement de Mathématique [Bruxelles] [ULB]
dc.contributor.authorDoignon, Jean-Paul
dc.date.accessioned2020-05-19T11:10:38Z
dc.date.available2020-05-19T11:10:38Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20756
dc.language.isoenen
dc.subjectBiordersen
dc.subjectNested relationsen
dc.subjectInterval ordersen
dc.subjectSemiordersen
dc.subjectNumerical representationsen
dc.subjectChain representationsen
dc.subjectWell-gradednessen
dc.subjectWeak gradednessen
dc.subject.ddc511en
dc.titleChain Representations of Nested Families of Biordersen
dc.typeChapitre d'ouvrage
dc.description.abstractenAmong the real-valued representations of nested families of biorders some representations reflect the nestedness of the family in a simple way. Calling them chain representations, we prove their existence in the finite and countably infinite cases. For the general case, we obtain chain representations in a well-chosen linearly ordered set. Although the existence of real-valued representations in general remains an open problem, our analysis answers questions left pending in the literature. It also leads to new proofs of classical theorems on the existence of a real representation for a single biorder, as well as for a single interval order. A combinatorial property of the set of all biorders from a finite set to another finite set plays a central role in the new proof; called weak gradedness, it is a particularization of well-gradedness which derives from a simpler argument.en
dc.identifier.citationpages143-169en
dc.relation.ispartofseriestitleStudies in Systems, Decision and Control (SSDC, volume 263)en
dc.relation.ispartoftitleMathematical Topics on Representations of Ordered Structures and Utility Theory : Essays in Honor of Professor Ghanshyam B. Mehtaen
dc.relation.ispartofeditorBosi, Gianni
dc.relation.ispartofeditorCampión, María J.
dc.relation.ispartofeditorCandeal, Juan C.
dc.relation.ispartofeditorIndurain, Esteban
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofdate2020-01
dc.relation.ispartofpages368en
dc.relation.ispartofurl10.1007/978-3-030-34226-5en
dc.subject.ddclabelPrincipes généraux des mathématiquesen
dc.relation.ispartofisbn978-3-030-34226-5en
dc.relation.forthcomingnonen
dc.identifier.doi10.1007/978-3-030-34226-5_7en
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2020-05-19T11:00:03Z
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