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 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 PublikoaWe 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.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.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 Un poco de orden: donde se cuentan mil zarandajas, tan impertinentes como necesarias, para el entendimiento desta grande historia(2021) Induráin Eraso, Esteban; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaEsta lección trata sobre el orden en matemáticas.Publication Open Access Why using topological and analytical methods in aggregation of fuzzy preferences?(2020) Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasThe Arrow’s Impossibility Theorem states that there is no function fusing individual preferences into a social one satisfying certain properties of 'common sense'. On the contrary, in some of the fuzzy extensions of the Arrovian model, possibility arises. We have developed a technique which has been able to prove new impossibility results in the fuzzy approach. In this poster, we will explain the fundaments of this technique and in which models we can apply it. This technique, is based on controlling the aggregation of fuzzy preferences through some aggregation functions of dichotomic preferences. For each fuzzy aggregation function, we get a family of dichotomic aggregation functions. Studying this family, we obtain information about the initial aggregation function. We will discuss why the fuzzy Arrovian models in which we can apply this technique are, in some sense, less fuzzy. Moreover, we will expose why we should use topological and analytical methods in the fuzzy models out of the scope of our technique.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 MatemáticasA 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.Publication Open Access Decomposition of fuzzy relations: an application to the definition, construction and analysis of fuzzy preferences(MDPI, 2023) Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBEIn this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences.Publication Open Access Semicontinuous planar total preorders on non-separable metric spaces(The Korean Mathematical Society, 2009) Campión Arrastia, María Jesús; Candeal, Juan Carlos; Induráin Eraso, Esteban; Matemáticas; MatematikaWe prove that every non-separable connected metric space can be endowed with a total preorder that is order-isomorphic to a nonrepresentable subset of the lexicographic plane and semicontinuous with respect to the metric topology.Publication Open Access Decomposition and arrow-like aggregation of fuzzy preferences(MDPI, 2020) Raventós Pujol, Armajac; 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 MatemáticasWe analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.Publication Open Access Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories(MDPI, 2024-08-13) Induráin Eraso, Esteban; Munárriz Iriarte, Ana; Sara Goyen, Martín Sergio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important possibility/impossibility results concerning criteria for extensions can be transferred to new results on scores. And conversely, conditions imposed a priori on scores can give rise to new extension criteria. This enhances and enriches both theories. We show examples of translations of classical results on extensions in the context of scores. Also, we state new results concerning the impossibility of finding a utility function representing some kind of extension order if some restrictions are imposed on the utility function considered as a score.
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