@article{Alsharari2025, 
author = {Fahad Alsharari and Ahmed O. M. Abubaker and Islam M. Taha},
title = {On    r-fuzzy soft    γ-open sets and fuzzy soft    γ-continuous functions with some applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {5285-5306},
keywords = {FS-topology, r-FS-γ-open set, FS-γ-closure operator, FS-γ-continuity, FS-weak γ-continuity, FS-γ-irresoluteness, r-FS-γ-normal space, r-FS-γ-connected set},
url = {https://www.sciopen.com/article/10.3934/math.2025244},
doi = {10.3934/math.2025244},
abstract = {In this paper, we defined and discussed a new class of fuzzy soft open (FS-open) sets, called    r-fuzzy soft    γ-open (   r-FS-   γ-open) sets in fuzzy soft topological spaces (FSTSs) based on fuzzy topologies in the sense of Šostak. The class of    r-FS-   γ-open sets is contained in the class of    r-FS-   β-open sets, and contains all    r-FS-semi-open and    r-FS-pre-open sets. However, we introduced the closure and interior operators with respect to the classes of    r-FS-   γ-closed and    r-FS-   γ-open sets, and studied some of their properties. Thereafter, we defined and studied some new FS-functions using    r-FS-   γ-open and    r-FS-   γ-closed sets, called FS-   γ-continuous (respectively (resp. for short) FS-   γ-irresolute, FS-   γ-open, FS-   γ-irresolute open, FS-   γ-closed, and FS-   γ-irresolute closed) functions. The relationships between these classes of functions were discussed with the help of some illustrative examples. We also explored and established the notions of FS-weakly (resp. FS-almost)    γ-continuous functions, which are weaker forms of FS-   γ-continuous functions. We showed that FS-   γ-continuity    ⟹ FS-almost    γ-continuity    ⟹ FS-weak    γ-continuity, but the converse may not be true. After that, we presented some new types of FS-separation axioms, called    r-FS-   γ-regular and    r-FS-   γ-normal spaces using    r-FS-   γ-closed sets, and investigated some properties of them. Finally, we introduced a new type of FS-connectedness, called    r-FS-   γ-connected sets using    r-FS-   γ-closed sets.}
}