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The problem of grey multi-attribute risk group decision-making is studied, when the attributive values are interval grey numbers and the attribute weights are unknown. Using grey incidence method of the grey system theory, relative deviation degree based on the optimum alternative group and the worst alternative group, a new method is proposed. It establishes an integrated optimization model dealing the weights of index based on that the deviation of group members is minimum and the deviation between two groups is maximum. By using the model, the attribute weights can be gotten. Then, based on subjective preferences of decision-maker group, synthetically deviations of each alternative to the optimum alternative group and the worst alternative group are calculated to determine the ranking order of alternatives. Finally, an example is given to show the feasibility and availability of this method.