Examples of fuzzy metrics and applications

Authors:
Valentín Gregori;Samuel Morillas;Almanzor Sapena
Affiliations:
Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain;Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain;Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

In this paper we present new examples of fuzzy metrics in the sense of George and Veeramani. The examples have been classified attending to their construction and most of the well-known fuzzy metrics are particular cases of those given here. In particular, novel fuzzy metrics, by means of fuzzy and classical metrics and certain special types of functions, are introduced. We also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection. Finally, we give an application of this type of fuzzy metrics to color image processing. We propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images, obtaining promising results. This application is also illustrative of how fuzzy metrics can be used in other engineering problems.