Abstract: With respect to the multiple attribute decision making problem with fuzzy preference relations on alternatives in form of incomplete complementary judgment matrix, a method is proposed to analyze the decision problem. The multiple attribute decision making problem is introduced and an optimization model is developed on the basis of incomplete complementary judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the appraisal values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.