FIA - Modelització Matemàtica Funcional i Aplicacions
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.
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.
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.
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.
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Articles de revista [44]
Recent Submissions
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Gaudí, geométricamente
(Real Sociedad Matemática Española, 2002-09)
Article
Restricted access - publisher's policyEn el 2002 celebramos el 150 aniversario del nacimiento de nuestro arquitecto más universal: Antoni Gaudí Cornet (1852-1926). Nuestro objetivo aquí es mostrar como la visión gaudiniana de la geometría es el resultado de ... -
A geometrical approach to aggregation
(2007-12)
Article
Restricted access - publisher's policyConsidering the family F of contour curves F = fh(x; y) = k) of an (idempotent) aggregation operator h in two variables as a one-parametric family of curves, the differential equation y0 = f(x; y) having F as general ... -
Permutable fuzzy consequence and interior operators and their connection with fuzzy relations
(2015-07-20)
Article
Open AccessFuzzy 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
(IOS Press, 2014)
Conference report
Open AccessThis 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
(Institute of Electrical and Electronics Engineers (IEEE), 2004)
Conference report
Restricted access - publisher's policyA 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
(-, 1992)
Conference report
Restricted access - publisher's policyA 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
(IEEE pub., 1993)
Conference report
Restricted access - publisher's policyA 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
(-, 2007)
Conference report
Open AccessLipschitzian 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
(-, 2007)
Conference report
Open AccessTwo 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
(IEEE Comp. Int. Soc., 2007)
Conference report
Open AccessLipschitzian 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
(Center for Soft Computing, 2008)
Conference report
Open AccessEn 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
(Center for Soft Computing, 2008)
Conference report
Open AccessEn 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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