Semiorders and continuous Scott–Suppes representations. Debreu’s Open Gap Lemma with a threshold
| dc.contributor.author | Estevan Muguerza, Asier | |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute for Advanced Research in Business and Economics - INARBE | en |
| dc.contributor.funder | Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, JIUPNA19-2022 | es |
| dc.date.accessioned | 2023-07-19T17:06:18Z | |
| dc.date.available | 2023-07-19T17:06:18Z | |
| dc.date.issued | 2023 | |
| dc.date.updated | 2023-07-19T16:57:55Z | |
| dc.description.abstract | The problem of finding a utility function for a semiorder has been studied since 1956, when the notion of semiorder was introduced by Luce. But few results on continuity and no result like Debreu’s Open Gap Lemma, but for semiorders, was found. In the present paper, we characterize semiorders that accept a continuous representation (in the sense of Scott–Suppes). Two weaker theorems are also proved, which provide a programmable approach to Open Gap Lemma, yield a Debreu’s Lemma for semiorders, and enable us to remove the open-closed and closed-open gaps of a set of reals while keeping the threshold. | en |
| dc.description.sponsorship | Asier Estevan acknowledges financial support from the Ministry of Science and Innovation of Spain under grants PID2020-119703RB-I00 and PID2021-127799NB-I00 as well as from the UPNA, Spain under grant JIUPNA19-2022. | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Estevan, A. (2023). Semiorders and continuous scott–suppes representations. Debreu’s open gap lemma with a threshold. Journal of Mathematical Psychology, 113, 102754. https://doi.org/10.1016/j.jmp.2023.102754 | en |
| dc.identifier.doi | 10.1016/j.jmp.2023.102754 | |
| dc.identifier.issn | 0022-2496 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/45804 | |
| dc.language.iso | eng | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartof | Journal of Mathematical Psychology 113 (2023) 102754 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI//PID2020-119703RB-I00/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI//PID2021-127799NB-I00/ | |
| dc.relation.publisherversion | https://doi.org/10.1016/j.jmp.2023.102754 | |
| dc.rights | © 2023 The Author(s). This is an open access article under the CC BY-NC-ND license. | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Continuity | en |
| dc.subject | Debreu's Open Gap Lemma | en |
| dc.subject | Scott-Suppes representation | en |
| dc.subject | Semiorders | en |
| dc.title | Semiorders and continuous Scott–Suppes representations. Debreu’s Open Gap Lemma with a threshold | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/publishedVersion | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e442a64a-b62e-4338-9a67-d7f4d9f12813 | |
| relation.isAuthorOfPublication.latestForDiscovery | e442a64a-b62e-4338-9a67-d7f4d9f12813 |