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Unit representation of semiorders I: Countable sets

Bouyssou, Denis; Pirlot, Marc (2020), Unit representation of semiorders I: Countable sets. https://basepub.dauphine.fr/handle/123456789/21098

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DBMP_SO_Denum.pdf (563.7Kb)
Type
Document de travail / Working paper
Date
2020
Series title
Preprint Lamsade
Published in
Paris
Metadata
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Author(s)
Bouyssou, Denis cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Pirlot, Marc
Université de Mons [UMons]
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.
Subjects / Keywords
Semiorder; Numerical Representation; Constant Threshold; Countable sets

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