Resumen de Métrica de Hausdorff en el ambiente difuso
Laura Victoria Forero Vega, Carlos Orlando Ochoa Castillo
- español
La distancia de Hausdorff corresponde, extiende y ajusta la noción de distancia entre subconjuntos no vacíos compactos en el ambiente de los espacios métricos, mas exactamenteen (Rn; du). De manera intuitiva, se ha establecido el concepto de conjunto como una colección distinta de elementos, esto es, un conjunto se determina vía la relación de pertenencia de un elemento de un universo al conjunto. La situación, por supuesto, es si pertenece o no pertenece; en un conjunto difuso a cada elemento del universo se le asocia con un grado de pertenencia, que es un numero entre 0 y 1. Los conjuntos difusos se establecen como una correspondencia entre cada elemento del universo y un grado de pertenencia. Al combinar estas dos teor´ıas, se genera un nuevo ambiente de estudio y de aplicación para las matem´aticas.
- English
Context: intuitively, the concept the set has been established as a collection of different elements, that is, a set is determined via the relationship of membership of an element of a universe as a whole. The situation, of course, is whether or does not belong; in a diffuse to each element subset of the universe it is associated with a degree of membership, which is a number between 0 and 1. The fuzzy subsets are established as a correspondence between each element of the universe and a degree of membership.Method: the study was based on previous work as articles or books, where authors present ideas about the importance of fuzzy subsets and the need to create with them new theories and spaces.Results: by combining two theories, a new study environment that allows state that corresponds Hausdorff distance, extends and adjusts the notion of distance between nonempty compact subsets in the environment of metrics spaces, more accurately generated in (Rn; du).Conclusions: the construction carried out allows a metric space with several qualities, where we can say that are the object consequence initial study.
