A new properties of fuzzy b-metric spaces

Metric spaces are specific types of topological spaces with pleasing “geometric” characteristics and they have a number of appealing properties and are commonly used in both pure and applied sciences. In this work, the structure of cartesian product space in the setting of a fuzzy b-metric space (Fb-M space) framework is introduced, which is an extension allows to create the large-scale structure for the space of the type fuzzy b-metric. The possibility of transferring some of the results and important features related to Fb-M space to this suggested space are discussed and demonstrated. The Cartesian product of two Fb-M spaces is proved as Fb-M space, this allows, to investigate and prove the topological expectation on the fuzzy product bmetric space. Furthermore, certain specific fuzzy b-metrics on F2 , and fuzzy Euclidean plane are obtained in this way.