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http://hdl.handle.net/2117/3771
Thu, 17 Apr 2014 19:23:31 GMT2014-04-17T19:23:31Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoSome 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 GMThttp://hdl.handle.net/2117/216202014-02-17T15:34:47ZCarmona, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, JeannoPermutability, Fuzzy consequence operator, Fuzzy preorder, Similarity relationComposition 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.Operadores de T-indistinguibilidad respecto a sumas ordinales
http://hdl.handle.net/2117/21615
Title: Operadores de T-indistinguibilidad respecto a sumas ordinales
Authors: Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge
Abstract: En este trabajo se estudia la clase de operadores de T-indistinguibilidad con T una suma ordinal. Mostramos que estos operadores de T-indistinguibilidad pueden pensarse como familias de operadores de indistinguibilidad respecto a t-normas arquimedianas. Se propone una interpretación en términos de clustering jerárquico.Mon, 17 Feb 2014 15:16:22 GMThttp://hdl.handle.net/2117/216152014-02-17T15:16:22ZBoixader Ibáñez, Dionís; Recasens Ferrés, JorgenoRelación borrosa, Operador de T-indistinguibilidad, T-norma, T-norma arquimediana, Suma ordinal, Clustering, Clustering jerárquico, Agregación jerárquicaEn este trabajo se estudia la clase de operadores de T-indistinguibilidad con T una suma ordinal. Mostramos que estos operadores de T-indistinguibilidad pueden pensarse como familias de operadores de indistinguibilidad respecto a t-normas arquimedianas. Se propone una interpretación en términos de clustering jerárquico.On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation
http://hdl.handle.net/2117/20905
Title: On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation
Authors: Carmona Cervelló, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
Abstract: 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.Tue, 03 Dec 2013 16:03:05 GMThttp://hdl.handle.net/2117/209052013-12-03T16:03:05ZCarmona Cervelló, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, JeannoIn 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
Title: Permutability of fuzzy consequence operators and fuzzy interior operators
Authors: Carmona, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
Abstract: 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.Tue, 03 Dec 2013 15:03:52 GMThttp://hdl.handle.net/2117/209032013-12-03T15:03:52ZCarmona, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, JeannoFuzzy closing, Fuzzy Consequence Operator, Fuzzy Interior Operator, Fuzzy Opening, PermutabilityIn 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
Title: Aggregation operators and quadric hypersurfaces
Authors: Recasens Ferrés, Jorge
Abstract: Aggregation operators that are quadric hypersurfaces are studied. The interest lays in the fact that the most popular aggregation operators are indeed quadric hypersurfaces.Tue, 08 Oct 2013 13:44:59 GMThttp://hdl.handle.net/2117/203362013-10-08T13:44:59ZRecasens Ferrés, JorgenoAggregation Operator, Idempotent, Symmetric, Quadric HypersurfaceAggregation 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
Title: Comparison of different algorithms of approximation by extensional fuzzy subsets
Authors: Mattioli Aramburu, Gabriel; Recasens Ferrés, Jorge
Abstract: 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.Tue, 08 Oct 2013 13:24:30 GMThttp://hdl.handle.net/2117/203352013-10-08T13:24:30ZMattioli Aramburu, Gabriel; Recasens Ferrés, JorgenoComputational Intelligence, Artificial Intelligence (incl. Robotics)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.Structural analysis of indistinguishability operators and related concepts
http://hdl.handle.net/2117/20143
Title: Structural analysis of indistinguishability operators and related concepts
Authors: Mattioli Aramburu, Gabriel; Recasens Ferrés, Jorge
Abstract: 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.Mon, 16 Sep 2013 16:47:02 GMThttp://hdl.handle.net/2117/201432013-09-16T16:47:02ZMattioli Aramburu, Gabriel; Recasens Ferrés, JorgenoSet theory, Artificial intelligence, Software engineeringGiven 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
Title: Searching for meaning on defuzzification
Authors: Recasens Ferrés, Jorge; Boixader Ibáñez, Dionís; Jacas Moral, Juan
Abstract: 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 operatorsWed, 04 Sep 2013 09:08:59 GMThttp://hdl.handle.net/2117/200952013-09-04T09:08:59ZRecasens Ferrés, Jorge; Boixader Ibáñez, Dionís; Jacas Moral, JuannoDefuzzification, fuzzy control, Approximate reasoning, Indistinguishability operator, Generator, Natural indistinguishabilityDefuzzification 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
Title: Upper and Lower Approximations of Fuzzy Sets
Authors: Boixader Ibáñez, Dionís; Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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 investigatedTue, 03 Sep 2013 11:00:48 GMThttp://hdl.handle.net/2117/200912013-09-03T11:00:48ZBoixader Ibáñez, Dionís; Jacas Moral, Juan; Recasens Ferrés, JorgenoIndistinguishability operator, Generator, Observable set, Upper approximation, Lower approximation, Rough sets, Modal logic, Closure operator, Fuzzy topologyThe 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
Title: The Length and Betweenness Relations of Indistinguishability Operators
Authors: Boixader Ibáñez, Dionís; Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: 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.Tue, 03 Sep 2013 10:50:43 GMThttp://hdl.handle.net/2117/200902013-09-03T10:50:43ZBoixader Ibáñez, Dionís; Jacas Moral, Juan; Recasens Ferrés, JorgenoIndistinguishability, Dimension, Betweenness relation, Transitive closure, Length, Decomposable relationThe 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.Effects of crop and weed densities on the interactions between barley and Lolium rigidum in several Mediterranean locations
http://hdl.handle.net/2117/20036
Title: Effects of crop and weed densities on the interactions between barley and Lolium rigidum in several Mediterranean locations
Authors: Izquierdo Figarola, Jordi; Recasens Ferrés, Jorge; Fernández-Quintanilla, C; Gill, G
Abstract: The effects of both barley and Lolium rigidum densities on weed growth and spike production and on crop yield were examined in five field experiments carried out in the Mediterranean drylands of Spain and Western Australia. The aim was to check the consistency of the competitiveness of the crop in different environmental and management conditions. L. rigidum reduced barley yields in most of the experiments (between 0 and 85%), the number of ears per m2 being the most affected. It was found that increasing the barley seeding rate did not reduce the crop losses but did limit weed biomass (between 5 and 61%) and spike production (between 24 and 85%). The variability observed in crop yield losses between sites and seasons was related to rainfall at the beginning of the season. The most sensitive component of yield to weed competition was the number of ears per plant.Wed, 31 Jul 2013 08:36:22 GMThttp://hdl.handle.net/2117/200362013-07-31T08:36:22ZIzquierdo Figarola, Jordi; Recasens Ferrés, Jorge; Fernández-Quintanilla, C; Gill, GnoInterference, Barley, Lolium rigidum, Crop yield, Mediterranean regionThe effects of both barley and Lolium rigidum densities on weed growth and spike production and on crop yield were examined in five field experiments carried out in the Mediterranean drylands of Spain and Western Australia. The aim was to check the consistency of the competitiveness of the crop in different environmental and management conditions. L. rigidum reduced barley yields in most of the experiments (between 0 and 85%), the number of ears per m2 being the most affected. It was found that increasing the barley seeding rate did not reduce the crop losses but did limit weed biomass (between 5 and 61%) and spike production (between 24 and 85%). The variability observed in crop yield losses between sites and seasons was related to rainfall at the beginning of the season. The most sensitive component of yield to weed competition was the number of ears per plant.Aggregation Operators Based on Indistinguishability Operators
http://hdl.handle.net/2117/19886
Title: Aggregation Operators Based on Indistinguishability Operators
Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge
Abstract: This article gives a new approach to aggregating assuming that there is an indistinguishability operator or similarity defined on the universe of discourse. The very simple idea is that when we want to aggregate two values a and b we are looking for a value l that is as similar to a as to b or, in a more logical language, the degrees of equivalence of l with a and b must coincide. Interesting aggregation operators on the unit interval are obtained from natural indistinguishability
operators associated to t-norms that are ordinal sums.Wed, 10 Jul 2013 11:33:14 GMThttp://hdl.handle.net/2117/198862013-07-10T11:33:14ZJacas Moral, Juan; Recasens Ferrés, JorgenoThis article gives a new approach to aggregating assuming that there is an indistinguishability operator or similarity defined on the universe of discourse. The very simple idea is that when we want to aggregate two values a and b we are looking for a value l that is as similar to a as to b or, in a more logical language, the degrees of equivalence of l with a and b must coincide. Interesting aggregation operators on the unit interval are obtained from natural indistinguishability
operators associated to t-norms that are ordinal sums.Transitivity of fuzzy relations under discretization
http://hdl.handle.net/2117/19659
Title: Transitivity of fuzzy relations under discretization
Authors: Boixader Ibáñez, Dionís; Recasens Ferrés, Jorge
Abstract: Fuzzy transitivity is a key property for many fuzzy relational structures, such as fuzzy preorders and equivalences. Theoretical models for practical problems which are based on fuzzy relations make use of continuous scales, mostly the unit interval [0, 1]. Practical implementation of these models though, involves their discretization into finite scales, which generally results in some loss of transitivity. In this paper we study if there are any transitivity preserving discretization strategies. Also, we evaluate the loss of transitivity in some commonly used discretization approaches.Tue, 25 Jun 2013 11:23:56 GMThttp://hdl.handle.net/2117/196592013-06-25T11:23:56ZBoixader Ibáñez, Dionís; Recasens Ferrés, JorgenoFuzzy equivalence, Fuzzy preorder, Fuzzy relation, Indistinguishability operator, L-relation, T-transitivityFuzzy transitivity is a key property for many fuzzy relational structures, such as fuzzy preorders and equivalences. Theoretical models for practical problems which are based on fuzzy relations make use of continuous scales, mostly the unit interval [0, 1]. Practical implementation of these models though, involves their discretization into finite scales, which generally results in some loss of transitivity. In this paper we study if there are any transitivity preserving discretization strategies. Also, we evaluate the loss of transitivity in some commonly used discretization approaches.Modelling a linguistic variable as a hierarchical family of partitions induced by an indistinguishability operator
http://hdl.handle.net/2117/19246
Title: Modelling a linguistic variable as a hierarchical family of partitions induced by an indistinguishability operator
Authors: Soto, De A R; Recasens Ferrés, Jorge
Abstract: This work shows a method to obtain a hierarchy of partitions on the universe [0,1] in such a way that each of them is compatible with a refinement of Lukasiewicz indistinguishability operator. The classes of the partition at a given level present a relation of antonymy between them. Moreover, the partition at a certain level can be seen as the refinement of a previous level by means of a class of linguistic modifiers. Due to this fact, they seem appropriate for modeling linguistic labels of a linguistic variable. The associated indistinguishability operators show the increasing granularity when the number of classes rises up.Wed, 15 May 2013 11:39:15 GMThttp://hdl.handle.net/2117/192462013-05-15T11:39:15ZSoto, De A R; Recasens Ferrés, JorgenoThis work shows a method to obtain a hierarchy of partitions on the universe [0,1] in such a way that each of them is compatible with a refinement of Lukasiewicz indistinguishability operator. The classes of the partition at a given level present a relation of antonymy between them. Moreover, the partition at a certain level can be seen as the refinement of a previous level by means of a class of linguistic modifiers. Due to this fact, they seem appropriate for modeling linguistic labels of a linguistic variable. The associated indistinguishability operators show the increasing granularity when the number of classes rises up.A reformulation of entropy in the presence of indistinguishability operators
http://hdl.handle.net/2117/19242
Title: A reformulation of entropy in the presence of indistinguishability operators
Authors: Recasens Ferrés, Jorge; Hernández, E
Abstract: This paper deals with the measurement of entropy when an indistinguishability relation on the set of events has been defined. Our approach states that entropy could be measured in terms of the observed distinguishability of the set of events. In this sense, the “observer paradigm” is introduced, and definitions for joint and conditional entropy under this paradigm are given. We also present some interesting properties and relationships with Shannon's entropy measure.Wed, 15 May 2013 10:58:59 GMThttp://hdl.handle.net/2117/192422013-05-15T10:58:59ZRecasens Ferrés, Jorge; Hernández, EnoThis paper deals with the measurement of entropy when an indistinguishability relation on the set of events has been defined. Our approach states that entropy could be measured in terms of the observed distinguishability of the set of events. In this sense, the “observer paradigm” is introduced, and definitions for joint and conditional entropy under this paradigm are given. We also present some interesting properties and relationships with Shannon's entropy measure.