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With respect to the group decision making problem with multi-granularity interval reciprocal linguistic judgment matrix, a method based on 2-tuple linguistic judgment matrix is proposed. In this method, the 2-tuple linguistic representation model and interval reciprocal linguistic judgment matrix are given. Then, a transformation function is given to uniform the multi-granularity linguistic terms by choosing a uniform linguistic term set. Based on the transformation function and the linguistic dominance degree of the alternatives, a procedure to solve the group decision making is given. Finally, the linguistic decision making model is applied to an example with multi-granularity linguistic term sets.