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Induráin Eraso, Esteban

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

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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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2017 - 20184
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Subject: Functional equations ×

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Now showing 1 - 4 of 4
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    PublicationOpen 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.
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    PublicationOpen 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.
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    PublicationOpen 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.
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    PublicationOpen 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 Publikoa
    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.