On Fuzzy γI-Continuity and γI-Irresoluteness via K-Fuzzy γI-Open Sets

In this article, we explored and investigated a novel class of fuzzy sets, called k-fuzzy γI-open (k-FγI-open) sets in fuzzy ideal topological spaces (FITSs) based on Sostak՚s sense. The class of k-FγI-open sets is contained in the class of k-fuzzy strong β-I-open (k-FSβI-open) sets and contains all k-fuzzy pre-I-open (k-FPI-open) sets and k-fuzzy semi-I-open (k-FSI-open) sets. We also introduced and studied the interior and closure operators with respect to the classes of k-FγI-open sets and k-FγI-closed sets. However, we defined and discussed novel types of fuzzy I-separation axioms using k-FγI-closed sets, called k-FγI-regular spaces and k-FγI-normal spaces. Thereafter, we displayed and studied the notion of fuzzy γI-continuity (FγI-continuity) using k-FγI-open sets. Furthermore, we presented and characterized the notions 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 investigated some new fuzzy γI-mappings via k-FγI-open sets and k-FγI-closed sets, called FγI-open mappings, FγI-closed mappings, FγI-irresolute mappings, FγI-irresolute open mappings, and FγI-irresolute closed mappings.