(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In the present paper, we introduce the notion of r-fuzzy soft δ-open sets in fuzzy soft topological spaces. Furthermore, we define and characterize the notions of fuzzy soft δ-closure (δ-interior) operators. After that, we explore the notions of fuzzy soft δ-continuous (semi-continuous and pre-continuous) functions, which are weaker forms of fuzzy soft continuity. We also study some properties of these functions along with their mutual relationships with the help of some problems. Moreover, we present a decomposition of fuzzy soft semi-continuity. Lastly, as a weaker form of fuzzy soft continuity, we define and study the notions of fuzzy soft almost (weakly) continuous functions. Also, we explore the notion of continuity in a very general setting called fuzzy soft (L, M, N, O)-continuity and introduce a historical justification.