A hybrid multi-stage decision-making method with probabilistic interval-valued hesitant fuzzy set for 3D printed composite material selection

The 3D printed composite material selection is of great interest due to its extensive application prospect and can be considered as a challenging multiple-criteria decision making (MCDM) issue. The hesitation and uncertainty of experts are difficult to measure, and the high degree of interaction among criteria is often overlooked in the decision process. In addition, composites are required to serve in harsh environments for various mechanical and industrial fields, resulting in the degradation of mechanical properties. In this study, a hybrid multi-stage decision-making method is developed to conduct 3D printed composite material selection in harsh environments. The theory of probabilistic interval-valued hesitant fuzzy set (PIVHFS) is proposed to characterize the decision-making information of experts, which can effectively quantify the assessment in uncertain environments. An integrated method that combines Choquet fuzzy integral and Shapley value is proposed to obtain the weight vector of criteria, which can reflect the mutual influence between criteria and their overall importance. The final decision-making result and the optimal alternative can be calculated by the PIVHFS-based Tomada de Decisão Interativa Multicritério and Technique for order preference by similarity to an ideal solution (TODIM-TOPSIS) method. An empirical application, i.e., 3D printed composites in the background of automotive chassis, is applied to validate the application of the proposed method. Comparative analysis, sensitivity analysis, and managerial implications are also conducted to illustrate the validity of the method. This paper provides a valuable tool for addressing the material selection issue of 3D printed composites from a multi-criteria perspective.