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20150305T10:36:09Z
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Onedimensional Tpreorders
http://hdl.handle.net/2117/26113
Title: Onedimensional Tpreorders
Authors: Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge
Abstract: 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.
Tue, 27 Jan 2015 12:59:57 GMT
http://hdl.handle.net/2117/26113
20150127T12:59:57Z
Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge
no
Dimension, Generator, Representation theorem, Strong complete Tpreorder, Tpreorder
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
Title: Indistinguishability operators generated by fuzzy numbers
Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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.
Tue, 03 Jun 2014 14:24:34 GMT
http://hdl.handle.net/2117/23140
20140603T14:24:34Z
Jacas Moral, Juan; Recasens Ferrés, Jorge
no
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
Title: Eigenvectors and generators of fuzzy relations
Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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.
Tue, 27 May 2014 14:43:31 GMT
http://hdl.handle.net/2117/23060
20140527T14:43:31Z
Jacas Moral, Juan; Recasens Ferrés, Jorge
no
Tnorm, Fuzzy relation, MaxT product, Tclosure, Teigenvector, Tindistinguishability operator, Generator
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
Title: Fuzzy numbers and equality relations
Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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.
Tue, 27 May 2014 14:30:58 GMT
http://hdl.handle.net/2117/23059
20140527T14:30:58Z
Jacas Moral, Juan; Recasens Ferrés, Jorge
no
Tnorm, Indistinguishability operator, Fuzzy number
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
Title: ETLipschitzian aggregation operators
Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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.
Wed, 14 May 2014 13:03:52 GMT
http://hdl.handle.net/2117/22986
20140514T13:03:52Z
Jacas Moral, Juan; Recasens Ferrés, Jorge
no
Aggregation Opoerator, Tindistinguishability Operator, Lipschitzian, Kernel
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
Title: Finding close Tindistinguishability operators to a given proximity
Authors: Garmendia Salvador, Luis; Recasens Ferrés, Jorge
Abstract: 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.
Wed, 14 May 2014 12:58:36 GMT
http://hdl.handle.net/2117/22985
20140514T12:58:36Z
Garmendia Salvador, Luis; Recasens Ferrés, Jorge
no
Proximity, Transitive Closure, Opening, Tindistinguishability Operator, Aggregation Operator, Quasi Arithmetic Mean, Representation Theorem
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
Title: Aggregation operators and the Lipschitzian condition
Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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.
Tue, 13 May 2014 14:39:39 GMT
http://hdl.handle.net/2117/22967
20140513T14:39:39Z
Jacas Moral, Juan; Recasens Ferrés, Jorge
no
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
Title: La Hoja de cálculo : un entorno para la enseñanza y estudio de relaciones borrosas
Authors: Casabó Gispert, Jorge Enrique; Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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.
Thu, 08 May 2014 14:41:42 GMT
http://hdl.handle.net/2117/22921
20140508T14:41:42Z
Casabó Gispert, Jorge Enrique; Jacas Moral, Juan; Recasens Ferrés, Jorge
no
Relaciones borrosas, Software educativo, Hoja de cálculo, Enseñanza de conjuntos borrosos
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
Title: Estructura de las similitudes
Authors: González del Campo, Ramón; Garmendia Salvador, Luis; Recasens Ferrés, Jorge
Abstract: 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.
Thu, 08 May 2014 13:11:55 GMT
http://hdl.handle.net/2117/22919
20140508T13:11:55Z
González del Campo, Ramón; Garmendia Salvador, Luis; Recasens Ferrés, Jorge
no
Relación borrosa, Mintransitividad, Similaridad
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.

Aproximación de Proximidades por Similitudes
http://hdl.handle.net/2117/22914
Title: Aproximación de Proximidades por Similitudes
Authors: Garmendia Salvador, Luis; Recasens Ferrés, Jorge
Abstract: En este trabajo se presenta un algoritmo para hallar una relaci´on de similitud próxima a una relación de proximidad (i.e.: una relación de tolerancia) R dada. La relación de similitud obtenida es más próxima a R que su clausura transitiva o cualquier opening transitivo de R.
Thu, 08 May 2014 12:16:39 GMT
http://hdl.handle.net/2117/22914
20140508T12:16:39Z
Garmendia Salvador, Luis; Recasens Ferrés, Jorge
no
Relación de Proximidad, Relación de Tolerancia, Relación de Similitud, Clausura Transitiva, Opening Transitivo
En este trabajo se presenta un algoritmo para hallar una relaci´on de similitud próxima a una relación de proximidad (i.e.: una relación de tolerancia) R dada. La relación de similitud obtenida es más próxima a R que su clausura transitiva o cualquier opening transitivo de R.

Approximating proximities by similarities
http://hdl.handle.net/2117/22906
Title: Approximating proximities by similarities
Authors: Garmendia Salvador, Luis; Recasens Ferrés, Jorge
Abstract: In this paper an algorithm to find a similarity close to a proximity or tolerance relation R is given. The obtained similarity is closer to R than its transitive closure or any transitive opening of R.
Thu, 08 May 2014 11:53:12 GMT
http://hdl.handle.net/2117/22906
20140508T11:53:12Z
Garmendia Salvador, Luis; Recasens Ferrés, Jorge
no
Proximity, Tolerance relation, Similarity, Transitive closure, Transitive opening
In this paper an algorithm to find a similarity close to a proximity or tolerance relation R is given. The obtained similarity is closer to R than its transitive closure or any transitive opening of R.

Approximate fuzzy preorders and equivalences
http://hdl.handle.net/2117/22889
Title: Approximate fuzzy preorders and equivalences
Authors: Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge
Abstract: Although Fuzzy Preorders and Fuzzy Equivalences are well established types of fuzzy relations, they are defined in terms of properties to be fulfilled in a crisp way. In this paper we relax those requirements by making them gradual in some way. As a result, a number of relations which are not strictly reflexive, symmetric or transitive with respect to any tnorm T, would be regarded as (Approximate) Fuzzy Preorders or Equivalences.
Wed, 07 May 2014 14:05:25 GMT
http://hdl.handle.net/2117/22889
20140507T14:05:25Z
Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge
no
Although Fuzzy Preorders and Fuzzy Equivalences are well established types of fuzzy relations, they are defined in terms of properties to be fulfilled in a crisp way. In this paper we relax those requirements by making them gradual in some way. As a result, a number of relations which are not strictly reflexive, symmetric or transitive with respect to any tnorm T, would be regarded as (Approximate) Fuzzy Preorders or Equivalences.

Powers of indistinguishability operators
http://hdl.handle.net/2117/22814
Title: Powers of indistinguishability operators
Authors: Mattioli Aramburu, Gabriel; Recasens Ferrés, Jorge
Abstract: The application of a tnorm more than one time to the same object can be seen as the modelization of a semantic reinforcement of it. From a mathematical viewpoint, this operation can be seen as powers. Depending on the properties the tnorm ful¿lls several interesting properties emerge. This work will study what is the effect of the application of powers to indistinguishability operators, sets of extensionals, upper and lower approximations. It will be proved that there is a tight relation between the powers of an indistinguishability and their respective sets of extensionals, upper and lower approximations, and how this can be interpreted from a semantic point of view.
Mon, 05 May 2014 13:21:45 GMT
http://hdl.handle.net/2117/22814
20140505T13:21:45Z
Mattioli Aramburu, Gabriel; Recasens Ferrés, Jorge
no
Extensional set, Indistinguishability operator, Lower approximation, Natural mean, Powers of atnorm, Upper approximation
The application of a tnorm more than one time to the same object can be seen as the modelization of a semantic reinforcement of it. From a mathematical viewpoint, this operation can be seen as powers. Depending on the properties the tnorm ful¿lls several interesting properties emerge. This work will study what is the effect of the application of powers to indistinguishability operators, sets of extensionals, upper and lower approximations. It will be proved that there is a tight relation between the powers of an indistinguishability and their respective sets of extensionals, upper and lower approximations, and how this can be interpreted from a semantic point of view.

Transitive closure of intervalvalued fuzzy relations
http://hdl.handle.net/2117/22748
Title: Transitive closure of intervalvalued fuzzy relations
Authors: González del Campo, Ramón; Garmendia Salvador, Luis; Recasens Ferrés, Jorge
Abstract: In this paper are introduced some concepts of intervalvalued fuzzy relations and some of their properties: reflexivity, symmetry, Ttransitivity, composition and local reflexivity. The existence and uniqueness of Ttransitive closure of intervalvalued fuzzy relations is proved. An algorithm to compute the Ttransitive closure of finite intervalvalued fuzzy relations is showed. Some properties and some examples is given for trepresentable and tpseudo representable generalized tnorms.
Tue, 29 Apr 2014 11:50:13 GMT
http://hdl.handle.net/2117/22748
20140429T11:50:13Z
González del Campo, Ramón; Garmendia Salvador, Luis; Recasens Ferrés, Jorge
no
Generalized tnorms, Intervalvalued Fuzzy Relations, Intervalvalued Fuzzy Sets, tnorms, trepresentable tnorms, Ttransitive closure
In this paper are introduced some concepts of intervalvalued fuzzy relations and some of their properties: reflexivity, symmetry, Ttransitivity, composition and local reflexivity. The existence and uniqueness of Ttransitive closure of intervalvalued fuzzy relations is proved. An algorithm to compute the Ttransitive closure of finite intervalvalued fuzzy relations is showed. Some properties and some examples is given for trepresentable and tpseudo representable generalized tnorms.

Some illustrative examples of permutability of fuzzy operators and fuzzy relations
http://hdl.handle.net/2117/21620
Title: Some illustrative examples of permutability of fuzzy operators and fuzzy relations
Authors: Carmona, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
Abstract: Composition of fuzzy operators often appears and it is natural to ask when the order of composition does not change the result. In previous papers, we characterized permutability in the case of fuzzy consequence operators and fuzzy interior operators. We also showed the connection between the permutability of the fuzzy relations and the permutability of their induced fuzzy operators. In this work we present some examples of permutability and non permutability of fuzzy operators and fuzzy relations in order to illustrate these results.
Mon, 17 Feb 2014 15:34:47 GMT
http://hdl.handle.net/2117/21620
20140217T15:34:47Z
Carmona, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
no
Permutability, Fuzzy consequence operator, Fuzzy preorder, Similarity relation
Composition of fuzzy operators often appears and it is natural to ask when the order of composition does not change the result. In previous papers, we characterized permutability in the case of fuzzy consequence operators and fuzzy interior operators. We also showed the connection between the permutability of the fuzzy relations and the permutability of their induced fuzzy operators. In this work we present some examples of permutability and non permutability of fuzzy operators and fuzzy relations in order to illustrate these results.