Some Applications of Generalized Fuzzy $\gamma ^*$-Closed Sets

Abstract

The generalized closed set plays an important role in the study of fuzzy topological spaces, and this paper is a prolongation of the idea of $g^*$-fuzzy closed set in the light of fuzzy $\gamma ^*$-open set in the same environment. In particular, this paper presents three different types of $g^*$-fuzzy closed sets, namely $\gamma ^*$-$g^*$-fuzzy closed set, $g^*$-$\gamma ^*$-fuzzy closed set, and $\gamma ^*$-$g^*$-$\gamma ^*$ fuzzy closed set via fuzzy $\gamma ^*$-open set in fuzzy topological spaces. Also, we establish the interrelationships among these newly defined fuzzy sets with the existing ones. As an application, we introduce and study some new classes of spaces called fuzzy $\gamma ^*$-${T_{1/2}}^*$ spaces, fuzzy ${T_{1/2}}^*$-$\gamma ^*$ space and fuzzy $\gamma ^*$-${T_{1/2}}^*$-$\gamma ^*$ space.