In this paper, we aim to develop a new type of neutrosophic fuzzy set called the star neutrosophic fuzzy set as a
generalization to star neutrosophic crisp set defined in by Salama et al.[8], and study some of its properties. Adedd
to, we introduce the notion of star neutrosophic fuzzy topological space as a generalization to some topological
consepts as star neutrosophic fuzzy closure, and star neutrosophic fuzzy interior. Finally, we extend the concepts of
fuzzy topological space, and intuitionistic fuzzy topological space to the case of star neutrosophic fuzzy sets.