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In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open  and generalized regular fuzzy irresolute closed maps in fuzzy  topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy irresolute maps are investigated. As a natural follow-up of the study of r-generalized regular fuzzy open sets, the concept of r-generalized regular fuzzy connectedness of a fuzzy set is introduced and studied.