# 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 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 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 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 MatemáticasShow more The 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.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 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 Aggregation of individual rankings through fusion functions: criticism and optimality analysis(IEEE, 2020) Bustince Sola, Humberto; Callejas Bedregal, Benjamin; Campión Arrastia, María Jesús; Silva, Ivanoska da; Fernández Fernández, Francisco Javier; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Santiago, Regivan; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasShow more Throughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the social choice where well-known impossibility results as the Arrovian ones are encountered and the decision-making approaches where the necessity of fusing rankings is unavoidable. Moreover it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice one should look for the maximal elements with respect to such orders defined on rankings IEEE.Show more 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 - INARBEShow more In 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.Show more 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 MatemáticasShow more Throughout 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.Show more Publication Open Access Strong negations and restricted equivalence functions revisited: an analytical and topological approach(Elsevier, 2021) Bustince Sola, Humberto; Campión Arrastia, María Jesús; Miguel Turullols, Laura de; Induráin Eraso, Esteban; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Throughout this paper, our main idea is to analyze the concepts of a strong negation and a restricted equivalence function, that appear in a natural way when dealing with theory and applications of fuzzy sets and fuzzy logic. Here we will use an analytical and topological approach, showing how to construct them in an easy way. In particular, we will also analyze some classical functional equation related to those key concepts.Show more