In this paper, we present a new method for handling fuzzy multiple criteria hierarchical group decision-making problems based on arithmetic operations and fuzzy preference relations of interval type-2 fuzzy sets. Because the time complexity of the proposed method is O(nk), where n is the number of criteria and k is the number of decision-makers, it is more efficient than Wu and Mendel's method, whose time complexity is O(mnk), where m is the number of α-cuts, n is the number of criteria and k is the number of decision-makers. Moreover, the proposed method can overcome another drawback of Wu and Mendel's method, i.e., it can handle evaluating values represented by nonnormal interval type-2 fuzzy sets. The proposed method provides us with a useful way to handle fuzzy multiple criteria hierarchical group decision-making problems.