Abstract
In this paper, we focus on finding the metric functions in a fuzzy metric space. After introducing the concept of a stratified function in a fuzzy metric space, we prove that the topology generated by the family of stratified functions coincides with the topology generated by the fuzzy metric. Moreover, we get the concrete form of metric function under some special conditions.
Highlights
Since Zadeh [1] first proposed fuzzy set theory in 1965, many researchers have defined concepts of fuzzy metric spaces and studied their properties in different ways [2,3,4]
Gregori and Veeramani proved in [7] that every GV-fuzzy metric M on X generates a topology τM which has as a base
We introduce the concept of a stratified function in a GV-fuzzy metric space
Summary
Since Zadeh [1] first proposed fuzzy set theory in 1965, many researchers have defined concepts of fuzzy metric spaces and studied their properties in different ways [2,3,4]. Many important topics about the classical metric spaces were developed to fuzzy metric spaces. In this process, it was found that the theory of fuzzy metric was very different from the classical theory of metric. Gregori and Romaguera [7] proved that there exists a GVfuzzy metric space which is not completable. The form of the metric function has not been explored in existing literature It is just the main goal of the present paper. We first introduce the concept of a stratified function in a fuzzy metric space which is slightly different from the GV-fuzzy metric space and show that the topology induced by the family of stratified functions is compatible with the metrizable topology.
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