On the Classical Sets of Sequences with Fuzzy b-Metric

Since the utilization of Zadeh s Extension Principle is quite difficult in practice, we prefer the idea of using the sum of the series of level sets. In this paper we present some classical sets of sequences of fuzzy numbers with respect to the notion of fuzzy b-metric. Also, we introduce the completeness of such spaces and derive the relationships between these sets and their classical forms. In addition, we use our results corresponding with series not only directly improve and generalize some results in metric spaces and b-metric spaces, and also expand and complement some previous results in fuzzy metric spaces with the level sets.