A new generalization of George & Veeramani-type fuzzy metric space

In this article, a concept of fuzzy $ \mathscr{F} $-metric space, which is a generalization of George & Veeramani-type fuzzy metric space, is introduced. Concepts of convergent sequence, Cauchy sequence, completeness etc. are given, and we study some properties in such spaces. Finally, some topological results are established.