On $ j $-fuzzy $ \gamma\mathcal{I} $-open sets with some applications

In this paper, we first introduced and studied a new class of fuzzy open sets, called $ j $-fuzzy $ \gamma\mathcal{I} $-open ($ j $-F$ \gamma\mathcal{I} $-open) sets on fuzzy ideal topological spaces ($ \mathcal{FITS}s $). The class of $ j $-F$ \gamma\mathcal{I} $-open sets is contained in the class of $ j $-fuzzy strong $ \beta $-$ \mathcal{I} $-open ($ j $-FS$ \beta\mathcal{I} $-open) sets and contains all $ j $-fuzzy pre-$ \mathcal{I} $-open ($ j $-FP$ \mathcal{I} $-open) sets and $ j $-fuzzy semi-$ \mathcal{I} $-open ($ j $-FS$ \mathcal{I} $-open) sets. We also defined and investigated the closure and interior operators with respect to the classes of $ j $-F$ \gamma\mathcal{I} $-closed sets and $ j $-F$ \gamma\mathcal{I} $-open sets. However, we explored and discussed novel types of fuzzy $ \mathcal{I} $-separation axioms using $ j $-F$ \gamma\mathcal{I} $-closed sets, called $ j $-F$ \gamma\mathcal{I} $-regular spaces and $ j $-F$ \gamma\mathcal{I} $-normal spaces. Thereafter, we displayed and investigated the concept of fuzzy $ \gamma\mathcal{I} $-continuity (F$ \gamma\mathcal{I} $-continuity) using $ j $-F$ \gamma\mathcal{I} $-open sets. Also, we presented and characterized the concepts of fuzzy weak $ \gamma\mathcal{I} $-continuity (FW$ \gamma\mathcal{I} $-continuity) and fuzzy almost $ \gamma\mathcal{I} $-continuity (FA$ \gamma\mathcal{I} $-continuity), which are weaker forms of F$ \gamma\mathcal{I} $-continuity. Moreover, we showed that F$ \gamma $$ \mathcal{I} $-continuity $ \Longrightarrow $ FA$ \gamma $$ \mathcal{I} $-continuity $ \Longrightarrow $ FW$ \gamma $$ \mathcal{I} $-continuity, but the converse may not be true. Finally, we defined and studied some new fuzzy $ \gamma\mathcal{I} $-mappings via $ j $-F$ \gamma\mathcal{I} $-open sets and $ j $-F$ \gamma\mathcal{I} $-closed sets, called F$ \gamma\mathcal{I} $-open mappings, F$ \gamma\mathcal{I} $-closed mappings, F$ \gamma\mathcal{I} $-irresolute mappings, F$ \gamma\mathcal{I} $-irresolute open mappings, and F$ \gamma\mathcal{I} $-irresolute closed mappings. The relationships between these classes of mappings were discussed with the help of some examples.