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The main purpose of this paper is to establish and prove some new common fixed point theorems for intuitionistic fuzzy maps in the context of (α,β)-cut sets of intuitionistic fuzzy sets on a complete metric space in association with the Hausdorff metric. Furthermore, the technique of Meir-Keeler (shortly, M-K) contraction is applied to obtain common fixed point of intuitionistic fuzzy compatible maps and fixed points of Kannan type intuitionistic fuzzy set-valued contractive mappings. Our results generalize M-K type fixed point theorem along with its various generalizations. Some nontrivial examples have been furnished in the support of the main results.