# 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 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 KonputazioaShow more We 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.Show more Publication Open Access Pointwise aggregation of maps: its structural functional equation and some applications to social choice theory(Elsevier, 2017) Miguel Turullols, Laura de; Campión Arrastia, María Jesús; Candeal, Juan Carlos; Induráin Eraso, Esteban; Paternain Dallo, Daniel; Automática y Computación; Matemáticas; Automatika eta Konputazioa; Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more We study a structural functional equation that is directly related to the pointwise aggregation of a finite number of maps from a given nonempty set into another. First we establish links between pointwise aggregation and invariance properties. Then, paying attention to the particular case of aggregation operators of a finite number of real-valued functions, we characterize several special kinds of aggregation operators as strictly monotone modifications of projections. As a case study, we introduce a first approach of type-2fuzzy sets via fusion operators. We develop some applications and possible uses related to the analysis of properties of social evaluation functionals in social choice, showing that those functionals can actually be described by using methods that derive from this setting.Show more Publication Open Access An axiomatic approach to finite means(Elsevier, 2018) Campión Arrastia, María Jesús; Candeal, Juan Carlos; García Catalán, Olga Raquel; Giarlotta, Alfio; 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 MatemáticasShow more In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications.Show more Publication Open Access Weightable quasi-metrics related to fuzzy sets(Hacettepe University (Turquía), 2018) Campión Arrastia, María Jesús; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Valero, Óscar; Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership function of a fuzzy set or from the disymmetry function of a quasi-metric.Show more Publication Open Access Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making(Elsevier, 2015) Miguel Turullols, Laura de; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Induráin Eraso, Esteban; Kolesárová, Anna; Mesiar, Radko; Matemáticas; Matematika; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more In this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.Show more Publication Open Access Geometrical aggregation of finite fuzzy sets(Elsevier, 2018) Campión Arrastia, María Jesús; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Lizasoain Iriso, María Inmaculada; Raventós Pujol, Armajac; Valero, Óscar; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y MatemáticasShow more A fuzzy set on a finite universe can be interpreted as a vector in a unit cube. This gives rise to a huge variety of approaches in order to aggregate finite fuzzy sets or to modify a given one. We analyze several geometrical methods and discuss possible applications in a multidisciplinary setting.Show more Publication Open Access Comparison meaningful operators and ordinal invariant preferences(Elsevier, 2015) Candeal, Juan Carlos; Induráin Eraso, Esteban; Matemáticas; MatematikaShow more The existence of a continuous and order-preserving real-valued function, for the class of continuous and ordinal invariant total preorders, defined on the Banach space of all bounded real-valued functions, which are in turn defined on a given set Ω, is characterized. Whenever the total preorder is nontrivial, the type of representation obtained leads to a functional equation that is closely related to the concept of comparison meaningfulness, and is studied in detail in this setting. In particular, when restricted to the space of bounded and measurable real-valued functions, with respect to some algebra of subsets of Ω, we prove that, if the total preorder is also weakly Paretian, then it can be represented as a Choquet integral with respect to a {0,1}-valued capacity. Some interdisciplinary applications to measurement theory and social choice are also considered.Show more 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 PublikoaShow more We 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.Show more Publication Open Access A survey on the mathematical foundations of axiomatic entropy: representability and orderings(MDPI, 2018) Campión Arrastia, María Jesús; Gómez Polo, Cristina; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Zientziak; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; CienciasShow more Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations.Show more 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 PublikoaShow more We 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.Show more