In this paper, we propose a new multiattribute decision making method based on interval-valued intuitionistic fuzzy sets, particle swarm optimization (PSO) techniques, and the evidential reasoning methodology. The proposed method uses the evidential reasoning methodology to construct objective functions of the programming models and uses PSO techniques to get optimal weights of the attributes to get the aggregated interval-valued intuitionistic fuzzy value of each alternative. Then, it calculates the transformed value of the obtained interval-valued intuitionistic fuzzy value of each alternative. The larger the transformed value, the better the preference order of the alternative. The proposed method can overcome the drawbacks of the existing methods for multiattribute decision making based on interval-valued intuitionistic fuzzy sets. It provides us with a useful way for multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques, and the evidential reasoning methodology.