The purpose of this paper is to study a fuzzy multiple attribute group decision making problem, where the attribute values are represented by trapezoidal fuzzy numbers, and the attribute weights are unknown completely, but each decision maker provides preference information on alternatives by the preference ordering. An assignment method is developed to solve this problem. Firstly, the contribution matrix of alternatives and the preference matrix of decision makers are created, then a quadratic programming is constructed to integrate the objective evaluations and the subjective preferences for determining the attribute weights. The ranking of alternatives or the best alternative(s) is obtained by constructing an assignment model to maximize the total contribution of alternatives. A numerical example is given to illustrate the proposed method.