Unit representation of semiorders II: The general case
Bouyssou, Denis; Pirlot, Marc (2020), Unit representation of semiorders II: The general case, Journal of Mathematical Psychology, 103, 102568. 10.1016/j.jmp.2021.102568
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Article accepté pour publication ou publiéDate
2020Journal name
Journal of Mathematical PsychologyVolume
103Number
102568Publisher
Elsevier
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Bouyssou, DenisLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Pirlot, Marc
Abstract (EN)
Necessary and sufficient 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. In contrast to the countable case, semiorders on uncountable sets that admit a strict unit representation do not necessarily admit a nonstrict unit representation, and conversely. By adapting the proof strategy used for strict unit representations, we establish a characterization of the semiorders that admit a nonstrict representation. Conditions for the existence of other special unit representations are also obtained.Subjects / Keywords
semiorder; numerical representation; constant threshold; uncountablesetsRelated items
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Bouyssou, Denis; Pirlot, Marc (2020) Document de travail / Working paper
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