Pankaj Chettri - Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.
Bishal Bhandari - Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.

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.

Generalized fuzzy topology, Fuzzy \mu^*-open (closed) set, Fuzzy \mu^*-continuous function, Fuzzy (\tau, \mu^*)-closed (open) function