Estevan Muguerza, Asier

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https://academica-e.unavarra.es/handle/2454/48984

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Estevan Muguerza

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Asier

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Estadística, Informática y Matemáticas

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INARBE. Institute for Advanced Research in Business and Economics

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0000-0002-8822-2438

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88759

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810060

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2018 - 201912020 - 20231
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Type: info:eu-repo/semantics/article × Subject: Semiorders ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    Partial representations of orderings
    (World Scientific, 2018) Bosi, Gianni; Estevan Muguerza, Asier; Zuanon, Magali; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner, avoiding any unnecessary information. For this purpose, the new concept of representability is developed by means of partial functions, so that other common definitions of representability (i.e. (Richter-Peleg) multi-utility, Scott-Suppes representability, … ) are now particular cases in which the partial functions are actually functions. The paper also presents a collection of examples and propositions showing the advantages of this kind of representations, particularly in the case of partial orders and semiorders, as well as some results showing the connections between distinct kinds of representations.
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    PublicationOpen Access
    Semiorders and continuous Scott–Suppes representations. Debreu’s Open Gap Lemma with a threshold
    (Elsevier, 2023) Estevan Muguerza, Asier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, JIUPNA19-2022
    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.