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To study the fuzzy and grey information in the problems of multi-attribute decision- making, the basic concepts of both the triangular fuzzy number and fuzzy grey number are given. Firstly, a new model of fuzzy grey multi-attribute decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the deviation degree is defined, and the algorithm of relative approximation value maximization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given.