On Fuzzy Soft α-open Sets, α-continuity, andα-compactness: Some Novel Results (European Journal of Pure and Applied Mathematics, 2024)
In this paper, we defined the notions of fuzzy soft α-interior (α-closure) operators via fuzzy soft topologies based on the sense of Sostak and studied some topological properties of them. Also, the notion of r-fuzzy soft α-connected sets was introduced and investigated. Thereafter, we defined and characterized the notions of fuzzy soft weakly (almost) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings. Moreover, we established that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. In addition, we investigated some properties of fuzzy soft α-continuity. It is also we showed that the composition  is fuzzy soft almost α-continuous mapping if  is fuzzy soft α-continuous mapping and  is fuzzy soft almost continuous mapping. Finally, some novel types of fuzzy soft compactness via r-fuzzy soft α-open sets were introduced and the relationships between them were explored with the help of some examples.
Keywords: Fuzzy soft topology; r-fuzzy soft α-open (α-closed) set; fuzzy soft α-interior (α-closure) operator; connectedness; fuzzy soft weakly (almost) α-continuity; compactness