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Unit representation of semiorders I: Countable sets

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Date
2020
Publisher city
Paris
Collection title
Preprint Lamsade
Link to item file
https://hal.archives-ouvertes.fr/hal-02918005
Dewey
Recherche opérationnelle
Sujet
Semiorder; Numerical Representation; Constant Threshold; Countable sets
URI
https://basepub.dauphine.fr/handle/123456789/21098
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)
This paper proposes a new proof of the existence of constant threshold representations of semiorders on countably infinite sets. The construction treats eachindifference-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 obtainan overall unit representation.

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