FIA és un grup que pretén aprofundir en la recerca dels mètodes i models matemàtics emprats en l'estudi de sistemes en els quals hi ha incertesa i/o imprecisió. En especial pel que fa a l'aplicació de tècniques de lògica borrosa, equacions funcionals i les lògiques no clàssiques en el Raonament Aproximat, la Presa de Decisions i la Mineria de Dades dins de l'àmbit de la Intel·ligència Artificial. La teoria d'equacions funcionals, a la qual el grup ha fet importants contribucions des de 1976, permet fer modelitzacions funcionals en lògica borrosa, connectors lògics, teoria de semigrups reals, teoria de dependència estadística, teoria d'índexos, geometria espacial, etc. El grup es proposa seguir aplicant aquestes tècniques en problemes borrosos, geomètrics i de representació. També es dona especial atenció als processos d'ensenyament de matemàtiques via modelització i aplicacions.

http://futur.upc.edu/FIA

FIA es un grupo de investigación dedicado a profundizar en la construcción de métodos y modelos matemáticos empleados en el estudio de sistemas en los cuales hay incertidumbre y/o imprecisión. En especial se aplican técnicas de lógica borrosa, ecuaciones funcionales y de lógicas no clásicas a Razonamiento Aproximado, Toma de Decisiones y Minería de Datos dentro del ámbito de la Inteligencia Artificial. La teoría de ecuaciones funcionales, a la cual el grupo ha hecho importantes contribuciones desde 1976, permite hacer modelizaciones funcionales en lógica borrosa, conectivas lógicas, teoría de semigrupos reales, teoría de dependencia estadística, teoría de índices, geometría espacial, etc. El grupo se propone seguir aplicando esta técnicas a problemas borrosos, geométricos y de representación. También se pone especial énfasis en los procesos de didáctica de las matemáticas vía modelización y aplicaciones.

http://futur.upc.edu/FIA

FM&AI is a group which pretends to make a deep research in the mathematical methods and models used in the study of systems in which uncertainty and/or vagueness is present, specially concerning the application of techniques of Fuzzy Logic, Functional Equations and non-classical logics to Approximate Reasoning, Decision Making and Data Mining in the realm of Artificial Intelligence. The theory of functional equations, to which the group has made important contributions since 1976, allows to make functional modellings in fuzzy logic, logical connectives, theory of real semi-groups, the theory of statistical dependence, the theory of indices, space geometry, etc. The group intends to continue applying these techniques in fuzzy, geometric and representation problems. Special attention will also be given to processes of mathematical education via modelling and applications.

http://futur.upc.edu/FIA

Recent Submissions

  • Permutable fuzzy consequence and interior operators and their connection with fuzzy relations 

    Carmona, Neus; Elorza Barbajero, Jorge; Recasens Ferrés, Jorge; Bragard, Jean (2015-07-20)
    Article
    Open Access
    Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order ...
  • One-dimensional T-preorders 

    Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge (IOS Press, 2014)
    Conference report
    Open Access
    This paper studies T-preorders by using their Representation Theorem that states that every T-preorder on a set X can be generated in a natural way by a family of fuzzy subsets of X. Especial emphasis is made on the study ...
  • Indistinguishability operators generated by fuzzy numbers 

    Jacas Moral, Juan; Recasens Ferrés, Jorge (Institute of Electrical and Electronics Engineers (IEEE), 2004)
    Conference report
    Restricted access - publisher's policy
    A new way to generate indistinguishability operators coherent with the underlying ordering structure of the real Dine is given in the sense that this structure should be compatible with the betweenness relation generated ...
  • Eigenvectors and generators of fuzzy relations 

    Jacas Moral, Juan; Recasens Ferrés, Jorge (-, 1992)
    Conference report
    Restricted access - publisher's policy
    A new geometric approach to the study of the eigenvectors is provided. The T-eigenvectors of a T-indistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde ...
  • Fuzzy numbers and equality relations 

    Jacas Moral, Juan; Recasens Ferrés, Jorge (IEEE pub., 1993)
    Conference report
    Restricted access - publisher's policy
    A general approach to the concept of fuzzy number associated to a generalized equality on the real line is given. As a result, the use of triangular and trapezoidal fuzzy numbers, among other types, is justified and a ...
  • ET-Lipschitzian aggregation operators 

    Jacas Moral, Juan; Recasens Ferrés, Jorge (-, 2007)
    Conference report
    Open Access
    Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and ...
  • Finding close T-indistinguishability operators to a given proximity 

    Garmendia Salvador, Luis; Recasens Ferrés, Jorge (-, 2007)
    Conference report
    Open Access
    Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T-transitive one where T is a continuous archimedean t-norm are given. The first one aggregates the transitive closure R ...
  • Aggregation operators and the Lipschitzian condition 

    Jacas Moral, Juan; Recasens Ferrés, Jorge (IEEE Comp. Int. Soc., 2007)
    Conference report
    Open Access
    Lipschitzian and kernel aggregation operators with respect to the natural T-indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ETLipschitzian, and is interpreted as a fuzzy point and ...
  • La Hoja de cálculo : un entorno para la enseñanza y estudio de relaciones borrosas 

    Casabó Gispert, Jorge Enrique; Jacas Moral, Juan; Recasens Ferrés, Jorge (Center for Soft Computing, 2008)
    Conference report
    Open Access
    En este trabajo se estudia la posibilidad de introduir conceptos de teoría de conjuntos borrosos en los currículos correspondientes a distintos niveles de enseñanza. Se hace especial hincapié en la enseñanza de las relaciones ...
  • Estructura de las similitudes 

    González del Campo, Ramón; Garmendia Salvador, Luis; Recasens Ferrés, Jorge (Center for Soft Computing, 2008)
    Conference report
    Open Access
    En este artículo se define formalmente el concepto de estructura de similaridad, se cuenta el número de estructuras de similaridades hasta dimensión 5, se propone una nomenclatura y un algoritmo que asigna una estructura ...

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