Abstract
In this paper we introduce a new type of fuzzy metric space and obtain several properties of it. Also some topological properties and boundedness are investigated. The notion of convergence of fuzzy sequences together with the notion of fuzzy cauchy sequences in a fuzzy metric space are discussed and some basic results related to these notions are investigated.
Highlights
The fuzzy set theory and applications has established as one of the most active areas of research in many branches of mathematics and engineering
Many authors have introduced the concept of fuzzy metric spaces in different ways and they studied the relation with fuzzy topology
Fuzzy metric spaces usually are introduced by means of the points in the crisp set X with fuzzy distance mapping or by using the fuzzy points in IX with a fuzzy distance between fuzzy points
Summary
The fuzzy set theory and applications has established as one of the most active areas of research in many branches of mathematics and engineering. Veeramani [9] in 1994, introduced a fuzzy metric space by considering points in the crisp set and a fuzzy distance between them. They gave several properties of these spaces many topological notions are discussed. The notion of a sequence is a good tool to study important topological properties such as the closure of a set and continuity of maps can be characterized using convergent sequences. We investigate the concept of fuzzy convergence and we define some types of Fuzzy boundedness in fuzzy metric spaces. The concept of complete fuzzy metric space is introduced and some relation among fuzzy convergence, F-boundedness and fuzzy compactness are investigated
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