On the sets of fuzzy-valued function with the level sets

In this paper, we construct the sets of bounded and continuous fuzzy-valued functions with the level sets. We investigate the relationships between these sets and their classical forms and give some properties including definitions, propositions and various kind of fuzzy distance functions. Furthermore, we study some of their properties like completeness, uniform convergence and differentiation and present two illustrative examples related to the complete and non-complete fuzzy metric spaces.