On j-Fuzzy γI-Open Sets with Some Applications

In this article, we first explored and investigated a new class of fuzzy sets, called j-fuzzy γI-open (j-FγI-open) sets in fuzzy ideal topological spaces (FITSs). The class of j-FγI-open sets is contained in the class of j-fuzzy strong β-I-open (j-FSβI-open) sets and contains all j-fuzzy pre-I-open (j-FPI-open) sets and j-fuzzy semi-I-open (j-FSI-open) sets. We also introduced and studied the closure and interior operators with respect to the classes of j-FγI-closed sets and j-FγI-open sets. However, we defined and discussed novel types of fuzzy I-separation axioms using j-FγI-closed sets, called j-FγI-regular spaces and j-FγI-normal spaces. Thereafter, we displayed and investigated the concept of fuzzy γI-continuity (FγI-continuity) using j-FγI-open sets. Moreover, we presented and characterized the concepts of fuzzy weak γI-continuity (FWγI-continuity) and fuzzy almost γI-continuity (FAγI-continuity), which are weaker forms of FγI-continuity. Finally, we introduced and studied some new fuzzy γI-mappings via j-FγI-open sets and j-FγI-closed sets, called FγI-open mappings, FγI-closed mappings, FγI-irresolute mappings, FγI-irresolute open mappings, and FγI-irresolute closed mappings.