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The relationship between the importance of criterion and the criterion aggregation function is discussed, criterion's weight and combinational weights between some criteria are defined, and a multi-criteria classification method with incomplete certain information and polynomial aggregation function is proposed. First, linear programming is constructed by classification to reference alternative set (assignment examples) and incomplete certain information on criterion's weights. Then the coefficient of the polynomial aggregation function and thresholds of categories are gained by solving the linear programming. And the consistency index of alternatives is obtained, the classification of the alternatives is achieved. The certain criteria's values of categories and uncertain criteria's values of categories are discussed in the method. Finally, an example shows the feasibility and availability of this method.