A Characterization of Strong and Weak Convergence in Fuzzy Metric Spaces
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Abstract
In this paper, we attempt to introduce the concept of fuzzy metric space and some of its properties, and we investigate the strong and weak convergence in fuzzy metric Spaces. Despite uncertainty in fuzzy random variables, crisp metrics have always been used. Here, we use the strong law of large numbers for fuzzy random variables in the fuzzy metric space for the bootstrap mean. Then the problem of constructing a satisfactory theory of fuzzy metric spaces has been investigated by several authors from different points of view. In particular, and by modifying a definition of fuzzy metric space given by Kramosil and Michalek, Georgeand Veeramani have introduced and studied the following interesting notion of a fuzzy metric space. A fuzzy metric space is such that is a set and is a function defined on satisfying certain axioms and is called a fuzzy metric in. Finally, we developed ideas that many of known strong and weak convergence theorems can easily be derived from the fuzzy metric Spaces.
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