Fuzzy $μ^*$-Open Set and Fuzzy $μ^*$-Continuous Function - Pankaj Chettri; Bishal Bhandari (Sahand Communications in Mathematical Analysis, 2023)
The prime goal of this article is to initiate the notion of fuzzy $μ^*$-open(closed) sets and fuzzy $μ^*$-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 $(τ, μ^*)$-open(closed) functions is introduced and their equivalent conditions with fuzzy $μ^*$-continuous functions are established.