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A Note on Candeal and Induráin’s Semiorder Separability Condition

Bouyssou, Denis; Pirlot, Marc (2020), A Note on Candeal and Induráin’s Semiorder Separability Condition, in Bosi, Gianni; Campión, María J.; Candeal, Juan C.; Indurain, Esteban, Mathematical Topics on Representations of Ordered Structures and Utility Theory : Essays in Honor of Professor Ghanshyam B. Mehta, Springer : Cham, p. 129-141. 10.1007/978-3-030-34226-5_6

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Type
Chapitre d'ouvrage
Date
2020
Book title
Mathematical Topics on Representations of Ordered Structures and Utility Theory : Essays in Honor of Professor Ghanshyam B. Mehta
Book author
Bosi, Gianni; Campión, María J.; Candeal, Juan C.; Indurain, Esteban
Publisher
Springer
Series title
Studies in Systems, Decision and Control (SSDC, volume 263)
Published in
Cham
ISBN
978-3-030-34226-5
Number of pages
368
Pages
129-141
Publication identifier
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
Faculté Polytechnique [UMONS]
Abstract (EN)
We show that the semiorder separability condition used by Candeal and Induráin in their characterization of semiorders having a strict representation with positive threshold can be factorized into two conditions. The first says that the trace of the semiorder must have a numerical representation. The second asserts that the number of “noses” in the semiorder must be finite or countably infinite. We discuss the interest of such a factorization.
Subjects / Keywords
Utility theory; Semiorders; Separability; Noses