In this paper, we introduce a notion of a parametric intuitionistic fuzzy metric space (in brief: p-intuitionistic fuzzy metric space) and prove that the parametric intuitionistic fuzzy metric induces a Hausdorff topology. We use this new notion to prove some fixed point results and some common fixed point results for a -contraction mapping and a pair of -contraction mappings, respectively.

intuitionistic fuzzy metric space, p-intuitionistic fuzzy metric space, -contraction maps, fixed points, common fixed point.