On a class of completable fuzzy metric spaces

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:
2010

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Abstract

In this paper we study some properties of a class of fuzzy metric spaces, in the sense of George and Veeramani, called strong. This class includes the class of stationary fuzzy metrics, and in particular, when the fuzzy metric is principal, we obtain a family of metrics which are compatible with the topology induced by the fuzzy metric. Also, we study some aspects of the completion of strong fuzzy metrics and we find a class of completable stationary fuzzy metrics which includes the class of stationary fuzzy ultrametrics.