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
TypeDocument de travail / Working paper
Series titlePreprint Lamsade
MetadataShow full item record
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
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 / KeywordsSemiorder; Numerical Representation; Constant Threshold; Countable sets
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