In the multi-criteria decision-making (MCDM) process, decision-makers with different risk attitudes may have different decision results. To address this issue and present decision-makers’ mentality, this paper introduces two mentality parameters. These parameters reflect the decision-makers’ risk attitudes in determining the membership and non-membership degrees of the evaluation information. In addition, the parameters demonstrate the risk attitude in terms of the hesitancy degree under interval-valued intuitionistic fuzzy information. Then, a new score function of interval-valued intuitionistic fuzzy numbers (IVIFNs) is proposed that uses the introduced mentality parameters. Meanwhile, certain properties of the proposed score function are discussed. Furthermore, the weighted comprehensive score value of IVIFNs is introduced, and an MCDM method is developed in an interval-valued intuitionistic fuzzy environment. Finally, a numerical example and comparative analyses are provided to illustrate the feasibility and effectiveness of the proposed method.
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