Some questions in fuzzy metric spaces

The George and Veeramani's fuzzy metric defined by $M^*(x,y,t)=\frac{min\{x,y\}+t}{max\{x,y\}+t}$ on $[0,\infty[$ (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 p...

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Bibliographic Details
Authors: Gregori Gregori, Valentín|||0000-0002-5983-6182, Miñana, Juan-José|||0000-0001-9835-0700, Morillas, Samuel|||0000-0001-9262-6139
Format: article
Publication Date:2012
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/36036
Online Access:https://riunet.upv.es/handle/10251/36036
Access Level:Open access
Keyword:Fuzzy metric spaces
Fuzzy metric completion
Strong (non-Archimedean) fuzzy metric
Principal fuzzy metric
MATEMATICA APLICADA
Description
Summary:The George and Veeramani's fuzzy metric defined by $M^*(x,y,t)=\frac{min\{x,y\}+t}{max\{x,y\}+t}$ on $[0,\infty[$ (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.