Document Type : Research Paper


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.


Main Subjects

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