Abstract: Analytic Hierarchy Process (AHP) is a utility theory based decision making technique, which researches on a premise that the decision making of complex problems can be handled by structuring them into simple and comprehensible hierarchical structure. However, AHP involves human subjective evaluation, which introduces vagueness that necessitates the use of decision making under uncertainty. The concept of Intuitionistic Fuzzy Sets (IFS) is the generalization of the concept of fuzzy set, which germane to uncertainty. The theory of IFS is well suited to dealing with vagueness. In this study, the concept of IFS is applied to AHP and to be called as IF-AHP as a method to handled vagueness in decision making. The aim of this study is to develop a new method for ranking multi-attribute group decision making problem using IFS and to quantify vagueness uncertainties in AHP using IFS for decision making problem. Several linear programming models are constructed to generate optimal weights for attributes. Feasibility and effectiveness of the proposed method are illustrated using a numerical evaluation.