Fuzzy Soft Topological Approaches Based on p-Fuzzy Soft Ω-Open Sets

In this study, we introduce new classes of fuzzy soft open sets, namely, p-FSΩ-open (respectively, p-FSΩP-open, p-FSΩS-open, p-FSΩα-open, and p-FSΩγ-open) sets in fuzzy soft topological spaces (FSTSs) based on fuzzy topologies in view of Šostak. We conduct a detailed investigation of the relationships among these classes of open sets, supported by carefully constructed illustrative problems. Furthermore, we propose and characterize the associated FSΩ-interior and FSΩ-closure operators. Subsequently, we define and analyze new classes of fuzzy soft functions based on p-FSΩ-open sets, referred to as FSΩ-continuous and FSΩ-irresolute functions within the framework of FSTSsS,ϑU and P,ζV. We also introduce and examine the notions of FSΩP-continuous, FSΩS-continuous, FSΩα-continuous, and FSΩγ-continuous functions, which constitute weaker forms of FSΩ-continuity. As an application, we demonstrate that these newly defined continuity concepts generalize, extend, and unify several existing results in the theory of FSTSs. Finally, we introduce and study the concepts of FSAΩ-continuity and FSWΩ-continuity as additional weaker variants of FSΩ-continuity. Moreover, we establish new separation axioms, termed p-FSΩ-normal and p-FSΩ-regular spaces, formulated via p-FSΩ-closed sets.