On $$g^*$$-Closed Sets in Fuzzy Topological Spaces

In this treatise, we propose a new type of closed set in fuzzy topological spaces called \(g^*\) fuzzy closed set, which is lying in between the fuzzy closed set and the generalized fuzzy closed set. Also, we study another class of fuzzy sets called \(\theta \)-\(g^*\) fuzzy closed sets which is weaker than \(\theta \)- fuzzy closed sets but stronger than \(\theta \)-g fuzzy closed sets and an interrelationships among these newly defined fuzzy closed sets along with the existing generalized fuzzy closed sets are established. Furthermore, the idea of fuzzy \(g^*\)-connectedness is introduced in the light of \(g^*\)-fuzzy closed sets. Finally, we define \({T_{1/2}}^*\)-space, \(^*T_{1/2}\)-space, \({_\theta T_{1/2}}^*\)-space and \({^*}_\theta T_{1/2}\)-space and some applications of these newly defined spaces are discussed.