Based on the conventional TOPSIS and in the light of the relative membership degree method, the calculation steps are given to solve the problem of multiple attribute decision- making with incomplete information on attribute weights. The key is the relative membership degree, which is obtained by means of the synthetically weighted distance. Then, the decision is made according to the relative membership degrees. By using this new method the difficulties that occur in ranking intervals in the traditional analysis methods are overcome. This shows that the relative membership degree method is better in selecting the best and ranking alternatives than the traditional TOPSIS method. Finally, practical calculations are given, which shows that the models are feasible and practical.