@article{Alsharari2025, 
author = {Fahad Alsharari and Jawaher Al-Mufarrij and Islam M. Taha},
title = {On    j-fuzzy    γ      I  -open sets with some applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20550-20570},
keywords = {fuzzy ideals, fuzzy topology, j-fuzzy γI-open set, fuzzy γI-continuity, fuzzy γI-irresoluteness},
url = {https://www.sciopen.com/article/10.3934/math.2025917},
doi = {10.3934/math.2025917},
abstract = {In this paper, we first introduced and studied a new class of fuzzy open sets, called    j-fuzzy    γ      I  -open (   j-F   γ      I  -open) sets on fuzzy ideal topological spaces (       F    I    T    S    s). The class of    j-F   γ      I  -open sets is contained in the class of    j-fuzzy strong    β-       I  -open (   j-FS   β      I  -open) sets and contains all    j-fuzzy pre-       I  -open (   j-FP       I  -open) sets and    j-fuzzy semi-       I  -open (   j-FS       I  -open) sets. We also defined and investigated the closure and interior operators with respect to the classes of    j-F   γ      I  -closed sets and    j-F   γ      I  -open sets. However, we explored and discussed novel types of fuzzy        I  -separation axioms using    j-F   γ      I  -closed sets, called    j-F   γ      I  -regular spaces and    j-F   γ      I  -normal spaces. Thereafter, we displayed and investigated the concept of fuzzy    γ      I  -continuity (F   γ      I  -continuity) using    j-F   γ      I  -open sets. Also, we presented and characterized the concepts of fuzzy weak    γ      I  -continuity (FW   γ      I  -continuity) and fuzzy almost    γ      I  -continuity (FA   γ      I  -continuity), which are weaker forms of F   γ      I  -continuity. Moreover, we showed that F   γ       I  -continuity    ⟹ FA   γ       I  -continuity    ⟹ FW   γ       I  -continuity, but the converse may not be true. Finally, we defined and studied some new fuzzy    γ      I  -mappings via    j-F   γ      I  -open sets and    j-F   γ      I  -closed sets, called F   γ      I  -open mappings, F   γ      I  -closed mappings, F   γ      I  -irresolute mappings, F   γ      I  -irresolute open mappings, and F   γ      I  -irresolute closed mappings. The relationships between these classes of mappings were discussed with the help of some examples.}
}