Articles de revista
http://hdl.handle.net/2117/3772
2015-11-25T16:37:27ZPermutable 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.
2015-07-21T09:09:29ZCarmona, NeusElorza Barbajero, JorgeRecasens Ferrés, JorgeBragard, JeanFuzzy 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.Transitive closure of interval-valued fuzzy relations
http://hdl.handle.net/2117/22748
Transitive closure of interval-valued fuzzy relations
González del Campo, Ramón; Garmendia Salvador, Luis; Recasens Ferrés, Jorge
In this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of interval-valued fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations is showed. Some properties and some examples is given for t-representable and t-pseudo representable generalized t-norms.
2014-04-29T11:50:13ZGonzález del Campo, RamónGarmendia Salvador, LuisRecasens Ferrés, JorgeIn this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of interval-valued fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations is showed. Some properties and some examples is given for t-representable and t-pseudo representable generalized t-norms.On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation
http://hdl.handle.net/2117/20905
On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation
Carmona Cervelló, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator, one from a fuzzy operator and a fuzzy relation and the other one from two fuzzy operators. The first one is an extension of the well-known fuzzy operator induced by a fuzzy relation through Zadeh’s compositional rule. Finally, we aggregate these operators using the quasi-arithmetic mean associated to a continuous Archimedean t-norm. The aim is to compare the operator induced by the quasi-arithmetic mean of the generators with the quasi-arithmetic mean of the generated operators.
2013-12-03T16:03:05ZCarmona Cervelló, NeusElorza, JorgeRecasens Ferrés, JorgeBragard, JeanIn this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator, one from a fuzzy operator and a fuzzy relation and the other one from two fuzzy operators. The first one is an extension of the well-known fuzzy operator induced by a fuzzy relation through Zadeh’s compositional rule. Finally, we aggregate these operators using the quasi-arithmetic mean associated to a continuous Archimedean t-norm. The aim is to compare the operator induced by the quasi-arithmetic mean of the generators with the quasi-arithmetic mean of the generated operators.Permutability of fuzzy consequence operators and fuzzy interior operators
http://hdl.handle.net/2117/20903
Permutability of fuzzy consequence operators and fuzzy interior operators
Carmona, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
In this paper we study the permutability of the composition of fuzzy consequence operators (fuzzy closings) and fuzzy interior operators (fuzzy openings). We establish several characterizations and we show the relation of permutability with the fuzzy closure and fuzzy interior of a fuzzy operator. We also study the connection between permutability and the preservation of the operator type through the composition. More precisely, when the composition of two openings is an opening and the composition of two closings is a closing.
2013-12-03T15:03:52ZCarmona, NeusElorza, JorgeRecasens Ferrés, JorgeBragard, JeanIn this paper we study the permutability of the composition of fuzzy consequence operators (fuzzy closings) and fuzzy interior operators (fuzzy openings). We establish several characterizations and we show the relation of permutability with the fuzzy closure and fuzzy interior of a fuzzy operator. We also study the connection between permutability and the preservation of the operator type through the composition. More precisely, when the composition of two openings is an opening and the composition of two closings is a closing.Aggregation operators and quadric hypersurfaces
http://hdl.handle.net/2117/20336
Aggregation operators and quadric hypersurfaces
Recasens Ferrés, Jorge
Aggregation operators that are quadric hypersurfaces are studied. The interest lays in the fact that the most popular aggregation operators are indeed quadric hypersurfaces.
2013-10-08T13:44:59ZRecasens Ferrés, JorgeAggregation operators that are quadric hypersurfaces are studied. The interest lays in the fact that the most popular aggregation operators are indeed quadric hypersurfaces.Comparison of different algorithms of approximation by extensional fuzzy subsets
http://hdl.handle.net/2117/20335
Comparison of different algorithms of approximation by extensional fuzzy subsets
Mattioli Aramburu, Gabriel; Recasens Ferrés, Jorge
How to approximate an arbitrary fuzzy subset by an adequate extensional one is a key question within the theory of Extensional Fuzzy Subsets. In a recent paper by the authors [19] different methods were provided to find good approximations. In this work these methods are compared in order to understand better the performance and improvement they give.
2013-10-08T13:24:30ZMattioli Aramburu, GabrielRecasens Ferrés, JorgeHow to approximate an arbitrary fuzzy subset by an adequate extensional one is a key question within the theory of Extensional Fuzzy Subsets. In a recent paper by the authors [19] different methods were provided to find good approximations. In this work these methods are compared in order to understand better the performance and improvement they give.Structural analysis of indistinguishability operators and related concepts
http://hdl.handle.net/2117/20143
Structural analysis of indistinguishability operators and related concepts
Mattioli Aramburu, Gabriel; Recasens Ferrés, Jorge
Given an indistinguishability operator E, it is possible to obtain the set of extensional fuzzy subsets HEHE and the respective operators of upper and lower approximations by extensional sets ¿E¿E and ¿E¿E. Reciprocally, given any of these objects, the initial indistinguishability operator E can be retrieved. It is well known that these concepts are in bijection. In this paper, we will prove that the relation underlying them is a lattice isomorphism. We will also consider further operators such as natural means and finally show the robustness of the results with respect to isomorphisms of t-norms.
2013-09-16T16:47:02ZMattioli Aramburu, GabrielRecasens Ferrés, JorgeGiven an indistinguishability operator E, it is possible to obtain the set of extensional fuzzy subsets HEHE and the respective operators of upper and lower approximations by extensional sets ¿E¿E and ¿E¿E. Reciprocally, given any of these objects, the initial indistinguishability operator E can be retrieved. It is well known that these concepts are in bijection. In this paper, we will prove that the relation underlying them is a lattice isomorphism. We will also consider further operators such as natural means and finally show the robustness of the results with respect to isomorphisms of t-norms.Searching for meaning on defuzzification
http://hdl.handle.net/2117/20095
Searching for meaning on defuzzification
Recasens Ferrés, Jorge; Boixader Ibáñez, Dionís; Jacas Moral, Juan
Defuzzification is an essential problem in fuzzy systems that it is always solved in a heuristic way. The aim of this work is to give a semantic interpretation to this process with the help of indistinguishability operators
2013-09-04T09:08:59ZRecasens Ferrés, JorgeBoixader Ibáñez, DionísJacas Moral, JuanDefuzzification is an essential problem in fuzzy systems that it is always solved in a heuristic way. The aim of this work is to give a semantic interpretation to this process with the help of indistinguishability operatorsUpper and Lower Approximations of Fuzzy Sets
http://hdl.handle.net/2117/20091
Upper and Lower Approximations of Fuzzy Sets
Boixader Ibáñez, Dionís; Jacas Moral, Juan; Recasens Ferrés, Jorge
The upper and lower approximations of a fuzzy subset with respect to an indistinguish-ability operator are studied. Their relations with fuzzy rough sets are also investigated
2013-09-03T11:00:48ZBoixader Ibáñez, DionísJacas Moral, JuanRecasens Ferrés, JorgeThe upper and lower approximations of a fuzzy subset with respect to an indistinguish-ability operator are studied. Their relations with fuzzy rough sets are also investigatedThe Length and Betweenness Relations of Indistinguishability Operators
http://hdl.handle.net/2117/20090
The Length and Betweenness Relations of Indistinguishability Operators
Boixader Ibáñez, Dionís; Jacas Moral, Juan; Recasens Ferrés, Jorge
The most common ways used to generate indistinguishability operators, namely
as transitive closure of reexive and symmetric fuzzy relation, via the Representation Theorem and as decomposable relations, is related for archimedean t-norms
introducing the notion of length of indistinguishability operators.
2013-09-03T10:50:43ZBoixader Ibáñez, DionísJacas Moral, JuanRecasens Ferrés, JorgeThe most common ways used to generate indistinguishability operators, namely
as transitive closure of reexive and symmetric fuzzy relation, via the Representation Theorem and as decomposable relations, is related for archimedean t-norms
introducing the notion of length of indistinguishability operators.