The aim of this paper is to introduce a new class of Fuzzy sets, namely the wg**-closed fuzzy set for Fuzzy topological spaces. This new class properly lies between the class of closed Fuzzy set and the class of wg-closed fuzzy set, we also introduce the application of wg**-closed fuzzy sets, the concept of fuzzy wg**-connectedness in Fuzzy topological spaces, and their properties are obtained.
