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 Ξ±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.