University of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Fuzzy $\mu^*$-Open Set and Fuzzy $\mu^*$-Continuous Function10511670580810.22130/scma.2023.1973748.1204ENPankajChettriDepartment of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.0000-0001-9092-1492BishalBhandariDepartment of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.0000-0003-0969-8620Journal Article20221118The 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.https://scma.maragheh.ac.ir/article_705808_827b0eda5f24f6238afd03acd622351c.pdf