Based on the concepts of interval type-2 fuzzy sets and intuitionistic fuzzy sets, this paper introduces the concept of interval type-2 intuitionistic fuzzy set that provides an extra dimension to intuitionistic fuzzy sets for the first time. Different arithmetic operations on interval type-2 intuitionistic fuzzy set are defined and a defuzzification method of interval type-2 intuitionistic fuzzy sets is developed for ranking purpose. Also, existing analytic hierarchy processes are further generalized with the introduction of interval type-2 intuitionistic fuzzy analytic hierarchy process to assess the relative importance among the alternatives in a convenient way under multi criteria decision-making environment. This process is efficient enough to evaluate the differences among the alternatives more prominently than the existing method that plays an important role in multi criteria decision-making contexts. Finally, a case example on supplier selection problem is considered and is solved to illustrate the applicability and validity of the proposed methodology.
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