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This paper studies the application of mathematical expectation-variance in the group decision making. First, the problem of group decision making based on different types of preference information is studied. The mutual transformation relations of preference information are researched. New and more reasonable transformation equations are acquired. Then a method of group decision making is given based on mathematical expectation-variance as an operator. Second, a method is presented for determining the attribute weights based on mathematical expectation-variance. Finally, a numerical example is given to show that the theoretical basis and calculation of the method is easy to be computed and implemented.