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Unit representation of semiorders II: The general case

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Date
2020
Publisher city
Paris
Collection title
Preprint Lamsade
Link to item file
https://hal.archives-ouvertes.fr/hal-02918017
Dewey
Recherche opérationnelle
Sujet
semiorder; numerical representation; constant threshold; uncountable sets
URI
https://basepub.dauphine.fr/handle/123456789/21099
Collections
  • LAMSADE : Publications
Metadata
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Author
Bouyssou, Denis
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Pirlot, Marc
Type
Document de travail / Working paper
Abstract (EN)
Necessary and suffcient 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. A direct adaptation of the same strategy allows us to prove a characterization of the semiorders that admit a nonstrict representation.

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