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For the situations that the preference information to attributes and estimating information to alternatives are expressed by intuitionistic fuzzy values, a new solution of the multiple attribute decision-making is given. Firstly, the solution of positive-ideal alternatives and negative-ideal alternatives are studied based on the traditional TOPSIS method. We give a method to choose the possible positive-ideal solution and the possible negative-ideal solution, and deal with the uncertainty information by entropy theory to get the only ideal alternatives. Secondly, the new solution of the best attribute weight vector is discussed. A new math model for solving the best attribute weight vector is given based on the isomorphism of intuitionistic fuzzy sets, and the process for solving multiple attribute decision-making is introduced. Finally, a practical example is illustrated to verify the effectiveness of this method.