The extended ELECTRE III group decision making method based on regret theory under probabilistic interval-valued hesitant fuzzy environments

The probabilistic interval-valued hesitant fuzzy sets (PIVHFSs), being able to generalize interval-valued hesitant fuzzy sets embedded with the decision makers (DMs)’ preferences for different elements, can depict uncertain decision information completely and precisely. Therefore, with this study, we propose an extended Elimination and Choice Translating Reality (ELECTRE) III method based on regret theory and Borda rule under a PIVHFS environment, which has the advantage of considering the regret psychology of the DMs and subordinate ranking orders. Using the proposed methodology, a fuzzy bidirectional projection measure is developed to overcome the shortcoming of unidirectional projection. The proposed method is validated by two numerical examples, and the effectiveness of the method is demonstrated through sensitivity and comparative analyses.