New fuzzy metric spaces based on gradual numbers

In this paper, we deal with special generalization of metric spaces by considering the distances between objects as gradual numbers. Firstly, the concept of gradual metric spaces is introduced. The new concept is a generalization of classical metric spaces and gradual linear normed spaces in the sense of Sadeqi and Azart. And then, basic concepts with respect to topology in gradual metric spaces are presented and their properties are discussed.