Abstract: In this Paper we introduce the concept of the fuzzy g*-closed set in fuzzy topological spaces. After the introduction of fuzzy sets by Zadeh in 1965 and fuzzy topology by Chang in 1967, several researches were conducted on the generalizations of the notions of fuzzy sets and fuzzy topology. In 1995, Thakur and Malviya extended the concept of g-closed sets in fuzzy topology. Many authors utilized fuzzy g-closed sets for the generalization of various fuzzy topological concepts in fuzzy topology. In 2010 Thakur and Mishra  introduced the concept of fuzzy g*-closed sets in fuzzy topology. In 2012 M. and Helen P. Introduced the concept of g**-closed sets in general topology. The present Paper extends the concept of g**-closed set due to Pauline M. and Helen P. In fuzzy topology and explore their study.
Keywords: Fuzzy topology, Fuzzy generalized closed sets, Fuzzy g**-closed set, Fuzzy g** -open set sets