FIA  Modelització Matemàtica Funcional i Aplicacions
http://hdl.handle.net/2117/3771
20151130T12:22:19Z

Permutable fuzzy consequence and interior operators and their connection with fuzzy relations
http://hdl.handle.net/2117/76237
Permutable fuzzy consequence and interior operators and their connection with fuzzy relations
Carmona, Neus; Elorza Barbajero, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
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 of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type.; We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh's compositional rule and the inf> composition. For this cases, we connect permutability of the fuzzy relations (using the sup* composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.
20150721T09:09:29Z
Carmona, Neus
Elorza Barbajero, Jorge
Recasens Ferrés, Jorge
Bragard, Jean
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 of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type.; We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh's compositional rule and the inf> composition. For this cases, we connect permutability of the fuzzy relations (using the sup* composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.

Onedimensional Tpreorders
http://hdl.handle.net/2117/26113
Onedimensional Tpreorders
Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge
This paper studies Tpreorders by using their Representation Theorem that states that every Tpreorder 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 of onedimensional Tpreorders (i.e.: Tpreorders that can be generated by only one fuzzy subset). Strong complete Tpreorders are characterized.
20150127T12:59:57Z
Boixader Ibáñez, Dionís
Recasens Ferrés, Jorge
This paper studies Tpreorders by using their Representation Theorem that states that every Tpreorder 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 of onedimensional Tpreorders (i.e.: Tpreorders that can be generated by only one fuzzy subset). Strong complete Tpreorders are characterized.

Indistinguishability operators generated by fuzzy numbers
http://hdl.handle.net/2117/23140
Indistinguishability operators generated by fuzzy numbers
Jacas Moral, Juan; Recasens Ferrés, Jorge
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 by the relation. A new way to generate indistinguishability operators coherent with the underlying ordering structure of the real line is given in the sense that this structure should be compatible with the between ness relation generated by the relation.
20140603T14:24:34Z
Jacas Moral, Juan
Recasens Ferrés, Jorge
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 by the relation. A new way to generate indistinguishability operators coherent with the underlying ordering structure of the real line is given in the sense that this structure should be compatible with the between ness relation generated by the relation.

Eigenvectors and generators of fuzzy relations
http://hdl.handle.net/2117/23060
Eigenvectors and generators of fuzzy relations
Jacas Moral, Juan; Recasens Ferrés, Jorge
A new geometric approach to the study of the eigenvectors is provided. The Teigenvectors of a Tindistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde (1985). This theorem states that every Tindistinguishability operator on a set X can be generated by a family of fuzzy subsets of X and, reciprocally, every family of fuzzy subsets of X generated a Tindistinguishability operator on X in a natural way. Some concepts related to Teigenvectors and generators of Tindistinguishabilities are reviewed, and their relation is studied. Some examples are given.
20140527T14:43:31Z
Jacas Moral, Juan
Recasens Ferrés, Jorge
A new geometric approach to the study of the eigenvectors is provided. The Teigenvectors of a Tindistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde (1985). This theorem states that every Tindistinguishability operator on a set X can be generated by a family of fuzzy subsets of X and, reciprocally, every family of fuzzy subsets of X generated a Tindistinguishability operator on X in a natural way. Some concepts related to Teigenvectors and generators of Tindistinguishabilities are reviewed, and their relation is studied. Some examples are given.

Fuzzy numbers and equality relations
http://hdl.handle.net/2117/23059
Fuzzy numbers and equality relations
Jacas Moral, Juan; Recasens Ferrés, Jorge
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 representation theo rem that allows the construction of indistinguishability operators on the real line based on tnorms is presented. The families of fuzzy numbers invariant under traslations are characterized.
20140527T14:30:58Z
Jacas Moral, Juan
Recasens Ferrés, Jorge
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 representation theo rem that allows the construction of indistinguishability operators on the real line based on tnorms is presented. The families of fuzzy numbers invariant under traslations are characterized.

ETLipschitzian aggregation operators
http://hdl.handle.net/2117/22986
ETLipschitzian aggregation operators
Jacas Moral, Juan; Recasens Ferrés, Jorge
Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A tnorm T is proved to be ET lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean tnorm T with additive generator t, the quasiarithmetic mean generated by t is proved to be the more stable aggregation operator with respect to T.
20140514T13:03:52Z
Jacas Moral, Juan
Recasens Ferrés, Jorge
Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A tnorm T is proved to be ET lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean tnorm T with additive generator t, the quasiarithmetic mean generated by t is proved to be the more stable aggregation operator with respect to T.

Finding close Tindistinguishability operators to a given proximity
http://hdl.handle.net/2117/22985
Finding close Tindistinguishability operators to a given proximity
Garmendia Salvador, Luis; Recasens Ferrés, Jorge
Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a Ttransitive one where T is a continuous archimedean tnorm are given. The first one aggregates the transitive closure R of R with a (maximal) Ttransitive relation B contained in R. The second one modifies the values of R or B to better fit them with the ones of R.
20140514T12:58:36Z
Garmendia Salvador, Luis
Recasens Ferrés, Jorge
Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a Ttransitive one where T is a continuous archimedean tnorm are given. The first one aggregates the transitive closure R of R with a (maximal) Ttransitive relation B contained in R. The second one modifies the values of R or B to better fit them with the ones of R.

Aggregation operators and the Lipschitzian condition
http://hdl.handle.net/2117/22967
Aggregation operators and the Lipschitzian condition
Jacas Moral, Juan; Recasens Ferrés, Jorge
Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A tnorm T is proved to be ETLipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean tnorm T with additive generator t, the quasiarithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T.
20140513T14:39:39Z
Jacas Moral, Juan
Recasens Ferrés, Jorge
Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A tnorm T is proved to be ETLipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean tnorm T with additive generator t, the quasiarithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T.

La Hoja de cálculo : un entorno para la enseñanza y estudio de relaciones borrosas
http://hdl.handle.net/2117/22921
La Hoja de cálculo : un entorno para la enseñanza y estudio de relaciones borrosas
Casabó Gispert, Jorge Enrique; Jacas Moral, Juan; Recasens Ferrés, Jorge
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 borrosas presentando un entorno Excel© como soporte docente y de experimentación.
20140508T14:41:42Z
Casabó Gispert, Jorge Enrique
Jacas Moral, Juan
Recasens Ferrés, Jorge
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 borrosas presentando un entorno Excel© como soporte docente y de experimentación.

Estructura de las similitudes
http://hdl.handle.net/2117/22919
Estructura de las similitudes
González del Campo, Ramón; Garmendia Salvador, Luis; Recasens Ferrés, Jorge
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 a cada similaridad.
20140508T13:11:55Z
González del Campo, Ramón
Garmendia Salvador, Luis
Recasens Ferrés, Jorge
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 a cada similaridad.