Person: Induráin Eraso, Esteban
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Induráin Eraso
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Esteban
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Estadística, Informática y Matemáticas
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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas
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0000-0002-1511-5658
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17
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Publication Embargo Binary relations coming from solutions of functional equations: orderings and fuzzy subsets(World Scientific Publishing Company, 2017) Campión Arrastia, María Jesús; Miguel Turullols, Laura de; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Abrísqueta Usaola, Francisco Javier; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equation. Applications to the numerical representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set.Publication Open Access New trends on the numerical representability of semiordered structures(EUSFLAT, 2012) Abrísqueta Usaola, Francisco Javier; Campión Arrastia, María Jesús; García Catalán, Olga Raquel; Miguel Velasco, Juan Ramón de; Estevan Muguerza, Asier; Induráin Eraso, Esteban; Zudaire Sarobe, Margarita; Agud, L.; Candeal, Juan Carlos; Díaz, S.; Martinetti, D.; Montes Rodríguez, Susana; Gutiérrez García, J.; Automática y Computación; Automatika eta KonputazioaWe introduce a survey, including the historical background, on di erent techniques that have recently been issued in the search for a characterization of the representability of semiordered structures, in the sense of Scott and Suppes, by means of a real-valued function and a strictly positive threshold of discrimination.Publication Open Access On the structure of acyclic binary relations(Springer, 2018) Rodríguez Alcantud, José Carlos; Campión Arrastia, María Jesús; Candeal, Juan Carlos; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe investigate the structure of acyclic binary relations from different points of view. On the one hand, given a nonempty set we study real-valued bivariate maps that satisfy suitable functional equations, in a way that their associated binary relation is acyclic. On the other hand, we consider acyclic directed graphs as well as their representation by means of incidence matrices. Acyclic binary relations can be extended to the asymmetric part of a linear order, so that, in particular, any directed acyclic graph has a topological sorting.Publication Open Access Open questions in utility theory(Springer, 2020) Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasThroughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.