Some questions in fuzzy metric spaces

Abstract

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.The authors wish to thank both the associated editors coordinating this submission and the reviewers for their insightful suggestions and comments which have been useful to increase the scientific quality and presentation of the paper. Also, the authors thank Dr. M. Melgosa, Dr. R. Huertas and Dr. L. Gomez-Robledo from the Department of Optics of University of Granada, for providing data, information and invaluable comments and suggestions. Valentin Gregori and Samuel Morillas acknowledge the support of Spanish Ministry of Education and Science under Grant MTM 2009-12872-C02-01. Samuel Morillas acknowledges the support of Research Project FIS2010-19839, Ministerio de Educacion y Ciencia (Espana) with European Regional Development Funds (ERDFs).Gregori Gregori, V.; Miñana Prats, JJ.; Morillas Gómez, S. (2012). Some questions in fuzzy metric spaces. Fuzzy Sets and Systems. 204:71-85. https://doi.org/10.1016/j.fss.2011.12.008718520