Unit representation of semiorders II: The general case
| Autor: | Denis Bouyssou, Marc Pirlot |
|---|---|
| Přispěvatelé: | Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision (LAMSADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université de Mons (UMons), Bouyssou, Denis, Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
uncountable sets Applied Mathematics 05 social sciences Representation (systemics) Semiorder numerical representation Function (mathematics) Characterization (mathematics) 16. Peace & justice [SHS.ECO]Humanities and Social Sciences/Economics and Finance constant threshold 050105 experimental psychology 0502 economics and business Countable set 0501 psychology and cognitive sciences Uncountable set semiorder [SHS.ECO] Humanities and Social Sciences/Economics and Finance Constant (mathematics) Unit (ring theory) General Psychology ComputingMilieux_MISCELLANEOUS 050205 econometrics Mathematics |
| Zdroj: | Journal of Mathematical Psychology Journal of Mathematical Psychology, Elsevier, 2021, pp.102568 Journal of Mathematical Psychology, Elsevier, 2021, 103, pp.102568. ⟨10.1016/j.jmp.2021.102568⟩ |
| ISSN: | 0022-2496 1096-0880 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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