Abstract
This article introduces the innovative concept of anti-fuzzy metric spaces and utilizes the property (E.A.) and Common limit range property of $\mathfrak{Q}$, we demonstrate the existence and uniqueness of a common fixed point in symmetric anti fuzzy metric spaces in this study. We discuss some novel ideas for a few mappings named R-weakly commuting of type $(\mathfrak{\mathfrak{J_P}})$ and weakly commuting of type $(\mathfrak{\mathfrak{J_P}})$ on an anti fuzzy metric space.
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