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To handle multicriteria fuzzy decision-making problems, a new multicriteria decision-making method is proposed in which the information about criteria's weights is not completely certain, and the criteria values of alternatives are Atanassov's intuitionistic fuzzy sets (A-IFSs). Using evidential reasoning algorithms, the criteria values are aggregated; receiving the overall A-IFS for alternatives and the distances between each alternative and the ideal, as well as anti-ideal alternative, are computed. Combining the incomplete certain information of weights, a nonlinear programming model is developed and resolved by particle swarm optimization algorithms to obtain the optimal criteria's weights. The corresponding decision-making procedure is given in detail. Finally, two examples are given to show the feasibility and availability of the proposed method.