Novel Categories of Spaces in The Frame of Fuzzy Soft Topologies

In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called -separation and -regularity axioms by using fuzzy soft -open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the -separation and -regularity axioms are harmonic and heredity property. Additionally, we examine the connections between -compactness and -separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology.