A first approach to an axiomatic model of multi-measures

We establish an axiomatic model of multi-measures, capturing some classes of measures studied in the fuzzy sets literature, where they are applied to only one or two arguments

Sobre medidas de T-Incompatibilidad para conjuntos borrosos de Atanassov

Continuando con el estudio sobre la in-compatibilidad entre conjuntos borrosos de Atanassov iniciado, en este articulo se presentan distintas formas de medir la incompatibilidad, bien sea considerando la familia de t-normas intuicionistas t-representables mediante t-normas y t-conormas conjugadas, respectivamente, con la t-norma y t-conorma de Lukasiewicz, o bien tomando otra familia de t-normas intuicionistas no representables. Por último, se muestran varios resultados en los que se evidencia la relación entre las distintas medidas de incompatibilidad propuestas

On the incompatibility between two AIFS

The purpose of this paper is to commence studying the incompatibility in the Atanassov's intuitionistic fuzzy sets framework. In order to do this, firstly we deal with the concept of T -incompatible sets, where T is an intuitionistic t- norm, relating it with the N-contradictory sets, where N is a intuitionistic fuzzy negation. Next, an axiomatic model for measuring T -incompatibility is introduced, and finally some methods for obtaining families of such measures are provided

Sobre la antonimia y su extensión a los conjuntos de Atanassov

Con este trabajo se inicia el estudio de la antonimia en el contexto de los conjuntos borrosos intuicionistas de Atanassov. Para ello, con el objetivo de afinar ciertos aspectos y poder trasladarlos a dicho campo, primero se retoma el concepto de antonimia y la obtención de antónimos en el contexto de los conjuntos borrosos, donde se analiza la construcción mediante involuciones. Después, se introducen los conceptos de conjuntos intuicionistas antónimos y de función antónimo obteniendo una familia de dichas funciones. Finalmente, se trata la relación de la antonimia en ambos campos y se proporcionan un resultado que las relacion

Self-Contradiction and Contradiction between two Atanassov's Intuitionistic Fuzzy Sets

The paper focuses on the study of the contradiction between two Atanassov's intuitionistic fuzzy sets. First, taking into account some characterizations obtained in previous papers, some functions are defined in order to measure the degrees of contradiction. Besides the principal properties of these measures are pointed out. Finally, some results relating self-contradiction and contradiction between two Atanassov's intuitionistic fuzzy sets are achieved

Measuring Contradiction between two AIFS

This paper is devoted to introduce an axiomatic model to distinguish what functions are suitable for measuring the degree of contradiction between two Atanassov's intuitionistic fuzzy sets. After stating the needed background, in section 2, we justify and present the axioms that a contradiction measure must satisfy, and the first examples are set out. After motivating the necessity of achieving some definition for modelling the continuity, in the next section we introduce the concepts of semicontinuity from below and semicontinuity from above for contradiction measures. Finally, in section 4, some families of contradiction measures are constructed

Measuring contradiction regarding a negation on AIFS

In, an axiomatic model for contradiction measures on Atanassov Intuitionistic fuzzy sets was presented; there, different kinds of those measures, depending on the continuity conditions required, were established. But in previous papers, not only the contradiction in general, but also the contradictions with respect to a given strong intuitionistic fuzzy negation were studied. This is due to the fact that in some applications, in order to fix a suitable model, not any negation is valid, but it is necessary to use a particular one. Thus, the problem of the axiomatization of the different types of contradiction measures regarding a given strong negation remained open. This is the main aim of the present work

Obtaining contradiction measure on intuitionistic fuzzy sets from fuzzy connectives

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of this paper is to construct some families of contradiction measures firstly using continuous t-norms and t-conorms, and secondly by means of strong negations. In both cases, we study the properties that they satisfy. These families are then classified according the different kinds of measures presented in the above paper

Un Modelo para Medir la N-Contradicción de Conjuntos Borrosos

En este artículo, se revisan los conceptos de conjuntos borrosos auto contradictorios y contradictorios respecto de una negación, extendiéndolos al marco, mas general, de las negaciones menos restrictivas, en lugar de considerar solo negaciones fuertes. A continuación, se establecen los axiomas mínimos que debe de verificar una función para que pueda ser considerada una medida de N-auto contradicción, y análogamente para una medida de N-contradicción, estableciéndose algunas relaciones entre ambos tipos de medidas. Finalmente, se introducen los axiomas para modelar la continuidad de las medidas cuando los conjuntos borrosos “crecen", ya análogamente, cuando “decrecen"; así mismo se proporcionan sendas familias de medidas de contradicción, de ambos tipos, que satisfacen una u otra propiedad

About t-norms on type-2 fuzzy sets.

Walker et al. defined two families of binary operations on M (set of functions of [0,1] in [0,1]), and they determined that, under certain conditions, those operations are t-norms (triangular norm) or t-conorms on L (all the normal and convex functions of M). We define binary operations on M, more general than those given by Walker et al., and we study many properties of these general operations that allow us to deduce new t-norms and t-conorms on both L, and M