International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/547 2020 2020 Port Said University, Faculty of Science, Department of Mathematics and Computer Science, Egypt A.A A.A.Salama Port Said University, Faculty of Engineering, Physics and Engineering Mathematics Department, Egypt Hewayda ElGhawalby Port Said University, Faculty of Engineering, Physics and Engineering Mathematics Department, Egypt A.M A.M.Nasr 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.   2019 2019 77 82 10.54216/IJNS.000203 https://www.americaspg.com/articleinfo/21/show/547