(𝔫, 𝔪)-Fuzzy e-Open Set in Šostak’s Sense with Applications via Double Fuzzy Topological Spaces

In this paper, we present and describe a new type of fuzzy open sets, called fuzzy (n,m)-e-open sets in double fuzzy topological spaces (DFT Ss,) based on Šostak’s approach. This type belongs to the group of fuzzy (n,m)-δ-β-open sets and includes all fuzzy (n,m)-δ-α-open sets, fuzzy (n,m)-δ-pre-open sets, and fuzzy (n,m)-δ-semi-open sets. We then explore the idea of DF-e-continuity between DFT Ss (Q,Γ,Γ*) and (K,T,T*). We also introduce and examine the concepts of DF-almost e-continuity and DF-weakly e-continuity, which are less strict than DF-e-continuity. Subsequently, we introduce and analyze new DF mappings through Fuzzy (n,m)-e-open and Fuzzy (n,m)-e-closed sets. Finally, we present and introduce some novel new types of DF-separation axioms, named Fuzzy (n,m)-e-regular and Fuzzy (n,m)-e-normal spaces, and we examine some of their properties.