Some questions in fuzzy metric spaces

  • Authors:

  • ValentíN Gregori;Juan-José MiòAna;Samuel Morillas

  • Affiliations:

  • Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n 46022 Valencia, Spain;Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n 46022 Valencia, Spain;Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n 46022 Valencia, Spain

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

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Abstract

The George and Veeramani's fuzzy metric defined by M^*(x,y,t)=(min{x,y}+t)/(max{x,y}+t) on [0,~[(the set of non-negative real numbers) has shown some advantages in front of classical metrics in the process of filtering images. In this paper we study from the mathematical point of view this fuzzy metric and other fuzzy metrics related to it. As a consequence of this study we introduce, throughout the paper, some questions relative to fuzzy metrics. Also, as another practical application, we show that this fuzzy metric is useful for measuring perceptual colour differences between colour samples.