## Abstract :

In this paper, as an application of fuzzy g^(##) - closed set in fuzzy topological spaces (fts), which is a class of closed fuzzy set. A fuzzy g^(##) - closed set is obtained by generalizing g^#- open fuzzy sets via fuzzy α-closure.We Introduced and investigated some new type of separation axioms namely, 〖fg〗^(##)-Regular Space, fg^(##)- Tychonoff space, 〖fg〗^(##)-Normal spaces,fg^(##)- Completely normal space in fts. The separation axiom provides a framework where the spaces have enough number of continues mappings. Also we have investigated some of their properties with counter examples.