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
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Psychology
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Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
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 / Keywordssemiorder; numerical representation; constant threshold; uncountablesets
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