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This paper studies the problems of multi-attribute group decision making with hybrid uncertainty information of fuzzy and grey. Firstly, the definition and algorithm of fuzzy grey number is presented, then a model of fuzzy grey multi-attribute group decision making is established. Thirdly, an optimization method of deviation degree is given to solve this new model. Finally, this model is applied to the decision making problem of risk investment. The application results show that this new model is effectual and feasible.