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

Contradiction versus Selfcontradiction in Fuzzy Logic

* This work is partially supported by CICYT (Spain) under project TIN 2005-08943-C02-001 and by UPM-CAM (Spain) under project R05/11240.Trillas et al. introduced in [7] and [8] the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Later, in [1] and [2] the necessity of determine not only the contradiction, but also the degree in that this property occurs, was considered. This paper takes up again these subjects, and firstly we study if there exists some connection between the two first notions. After that, taking into account that self- contradiction of a fuzzy set could be understood as the contradiction with itself, and starting from the degrees of contradiction between two fuzzy sets proposed in [5], we obtain degrees of self-contradiction. Finally, preservation of some intuitive properties both in the use of connectives and in the obtaining of new knowledge throughout compositional rule of inference, are tested

On the Coherence Between Probability and Possibility Measures

* This paper is supported by CICYT (Spain) under Project TIN 2005-08943-C02-01.The purpose of this paper is to study possibility and probability measures in continuous universes, taking different line to the one proposed and dealt with by other authors. We study the coherence between the probability measure and the possibility measure determined by a function that is both a possibility density and distribution function. For this purpose, we first examine functions that satisfy this condition and then we anlyze the coherence in some notable probability distributions cases

Programa de tratamiento de drogas bajo supervisión judicial a la luz de los fines de la pena y de una política criminal humanista. Análisis del Proyecto de ley: Ley de Justicia Restaurativa n.° 19 935

Mediante el Proyecto de Ley n.° 19 935 denominado Ley de Justicia Restaurativa, se pretende otorgar rango legal al ya existente Programa de Tratamiento de Drogas bajo Supervisión Judicial (PTDJ), que se implementó desde el año 2013 sobre la plataforma del Programa de Justicia Restaurativa del Poder Judicial, impulsado en su momento por el Instituto Costarricense sobre Drogas (ICD) desde el Programa de Tribunales de Drogas de las Américas de la Organización de Estados Americanos (OEA), coordinado por la Secretaría Ejecutiva de la Comisión Interamericana para el Control del Abuso de Drogas (CICAD), la Secretaría de Seguridad Multidimensional de la Organización de los Estados Americanos y con el apoyo financiero del Gobierno de Canadá. El Proyecto de ley dispone como objetivo general la instauración del programa de justicia restaurativa como medio alternativo de elaboración, aplicación y evaluación de políticas y procesos de solución de conflictos, en aras de conseguir la paz social, restaurar el tejido social, la prevención especial y general del delito y mantener la seguridad ciudadana. También ha dispuesto lograr la humanización, a través de un abordaje integral de las partes, apoyar a la víctima en el proceso de reparación del daño sufrido y resocializar y reinsertar a las personas ofensoras a la comunidad. Asimismo, promover la participación ciudadana en la solución de conflictos. Ante el fenómeno de la drogadicción, se implanta como medio alternativo para solucionar el conflicto y abordar la enfermedad adictiva de quienes delinquen en razón de esta condición con un enfoque biopsicosocial. De forma innovadora, además de ser el mecanismo para la homologación de medidas alternas, introduce el PTDJ como pena alternativa a la prisión.Universidad Estatal a Distancia de Costa Ric

Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures

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

A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained

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

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