A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing theHarmonized European Time Use Surveys system. Under such a unified framework,the first Time Use Survey of national scope was conducted in Spain during 2002–03. The aim of these surveys is to understand human behavior and the lifestyle ofpeople. Time allocation data are of compositional nature in origin, that is, they aresubject to non-negativity and constant-sum constraints. Thus, standard multivariatetechniques cannot be directly applied to analyze them. The goal of this work is toidentify homogeneous Spanish Autonomous Communities with regard to the typicalactivity pattern of their respective populations. To this end, fuzzy clustering approachis followed. Rather than the hard partitioning of classical clustering, where objects areallocated to only a single group, fuzzy method identify overlapping groups of objectsby allowing them to belong to more than one group. Concretely, the probabilistic fuzzyc-means algorithm is conveniently adapted to deal with the Spanish Time Use Surveymicrodata. As a result, a map distinguishing Autonomous Communities with similaractivity pattern is drawn.Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations

La borrosidad como epistemología de la interacción social: algunos alcances y potencialidades

En este trabajo se describen la teoría de los conjuntos borrosos de L. A. Zadeh(antecedentes, características e implicaciones) y las áreas en las que se ha aplicado laborrosidad en psicología y psicología social (desarrollo evolutivo, procesamiento deestímulos, percepción de la información, prototipos y otras aplicaciones). A partir de esto,se sugiere cómo la borrosidad podría ser útil en el estudio de la interacción social,asumiendo el carácter simultáneamente vago y preciso de la realidad, y la utilización deconceptos como la noción de sí mismo desde una visión compleja, que considere, desde laperspectiva del pluralismo, diversas posturas teóricas y metodológicas.

Aplicación de una técnica operativa con carácter discriminatorio en los procesos de selección de personal

Existen técnicas clásicas cuya función es seleccionar aquellas personas que son idóneas para un determinado puesto de trabajo. El punto fundamental consiste en adaptar una persona a un perfíl de tareas que esa persona debe desarrollar y al mismo tiempo esa persona debe sentirse parte integrante de la empresa, para conseguirlo, en el presente trabajo expondremos una nueva técnica para la selección de personal ejecutivo y basada en la teoría de los subconjuntos borrosos dentro de las nuevas técnicas operativas de gestión.

Lattices for 3-Dimensional Fuzzy Data generated by Fuzzy Galois Connections

Vagueness and high dimensional space data are usual features of current data. The paper is an approach to identify conceptual structures among fuzzy three dimensional data sets in order to get conceptual hierarchy. We propose a fuzzy extension of the Galois connections that allows to demonstrate an isomorphism theorem between fuzzy sets closures which is the basis for generating lattices ordered-sets

Anàlisis del modelo de la telaraña en contexto de incertidumbre

In the present work the behavior of a model acquaintance of market is analyzed with an only one, in that is considered that the parameters that tie the variables that it incorporates the pattern come expressed through uncertain magnitudes. The objective of the study consists on the analysis of the balance from the hypotheses of established uncertainties

Extending the roughness of the data via transitive closures of similarity indexes

One main assumption in the theory of rough sets applied to information tables is that the elements that exhibit the same information are indiscernible (similar) and form blocks that can be understood as elementary granules of knowledge about the universe. We propose a variant of this concept defining a measure of similarity between the elements of the universe in order to consider that two objects can be indiscernible even though they do not share all the attribute values because the knowledge is partial or uncertain. The set of similarities define a matrix of a fuzzy relation satisfying reflexivity and symmetry but transitivity thus a partition of the universe is not attained. This problem can be solved calculating its transitive closure what ensure a partition for each level belonging to the unit interval [0,1]. This procedure allows generalizing the theory of rough sets depending on the minimum level of similarity accepted. This new point of view increases the rough character of the data because increases the set of indiscernible objects. Finally, we apply our results to a not real application to be capable to remark the differences and the improvements between this methodology and the classical one

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing the Harmonized European Time Use Surveys system. Under such a unified framework, the first Time Use Survey of national scope was conducted in Spain during 2002– 03. The aim of these surveys is to understand human behavior and the lifestyle of people. Time allocation data are of compositional nature in origin, that is, they are subject to non-negativity and constant-sum constraints. Thus, standard multivariate techniques cannot be directly applied to analyze them. The goal of this work is to identify homogeneous Spanish Autonomous Communities with regard to the typical activity pattern of their respective populations. To this end, fuzzy clustering approach is followed. Rather than the hard partitioning of classical clustering, where objects are allocated to only a single group, fuzzy method identify overlapping groups of objects by allowing them to belong to more than one group. Concretely, the probabilistic fuzzy c-means algorithm is conveniently adapted to deal with the Spanish Time Use Survey microdata. As a result, a map distinguishing Autonomous Communities with similar activity pattern is drawn. Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

Aplicación de la matemática borrosa a la gestión deportiva.

Aproximación a la gestión deportiva a partir de la matemática borrosa. Mediante esta matemática se aporta una serie de algoritmos que permiten establecer la idoneidad del deportista y las cualidades que ha de reunir para ser considerado adecuado en las distintas posiciones. La teoría de conjuntos borrosos tiene su origen en los años 20 y es en las últimas décadas cuando está adquiriendo una mayor aplicación.

El comentario de textos : la novela.

Resumen basado en el de la publicación

Lógica difusa : una nueva epistemología para las Ciencias de la Educación.

Resumen tomado de la publicación. Monográfico con el título: La tarea de enseñar: atraer, formar, retener y desarrollar buen profesorado. Texto completo sólo disponible en el CD anexo o en la versión en línea

Las prácticas de justificación en el aula de matemáticas.

Resumen basado en el de la publicación

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations