$$s_{p}-$$ s p - Closedness and $$s_{p}-$$ s p - convergent sequences in IFMS and its generalization to $${\mathscr {L}}$$ L -fuzzy metric space

The aim of the present article is to introduce the concepts of $$s_{p}-$$ convergent sequence in generalized intuitionistic fuzzy metric spaces, i.e., $${\mathscr {L}}$$ -fuzzy metric spaces and analyze relations of convergence, $$s_{p}-$$ convergence, $$s_{\infty }-$$ convergence and $$st-$$ convergence in $${\mathscr {L}}$$ -fuzzy metric spaces. Further, we examine $$s_{p}-$$ convergence, $$s_{\infty }-$$ convergence and $$st-$$ convergence using the subsequence of convergent sequence for above-stated spaces. We finally define $$s_{p}-$$ closed sets, $$s_{\infty }-$$ closed sets and $$st-$$ closed sets in intuitionistic fuzzy metric spaces and investigate relations of them.