Person:
Induráin Eraso, Esteban

person.page.identifierURI

https://academica-e.unavarra.es/handle/2454/49278

Last Name

Induráin Eraso

First Name

Esteban

person.page.departamento

Estadística, Informática y Matemáticas

person.page.instituteName

InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

ORCID

0000-0002-1511-5658

person.page.upna

17

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Now showing 1 - 10 of 22

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 Publikoa
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.
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 Matemáticas
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.
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 Publikoa
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.
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 Matematika
Esta lección trata sobre el orden en matemáticas.
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 - INARBE
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.
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 Publikoa
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.
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 Matemáticas
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.
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 Matemáticas
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.
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 - INAMAT2
We 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.
Open Access
Comparison meaningful operators and ordinal invariant preferences
(Elsevier, 2015) Candeal, Juan Carlos; Induráin Eraso, Esteban; Matemáticas; Matematika
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.