Fuzzy $\mu^*$-Open Set and Fuzzy $\mu^*$-Continuous Function

The prime goal of this article is to initiate the notion of fuzzy    $\mu^*$-open(closed) sets and fuzzy $\mu^*$-continuous functions and characterize  them. These concepts are defined in a fuzzy topological space in presence of a  generalized fuzzy topology, which becomes a new tool to study fuzzy topological spaces. It is observed that this class of fuzzy sets fail to form a fuzzy topology but it form a generalized fuzzy topology. Furthermore, the relationship of these fuzzy sets and fuzzy continuity with some existing fuzzy notions are established. Also the notion of fuzzy $(\tau, \mu^*)$-open(closed) functions is introduced and their equivalent conditions with  fuzzy $\mu^*$-continuous functions are established.