Multi-criteria group decision-making with extended ELECTRE III method and regret theory based on probabilistic interval-valued intuitionistic hesitant fuzzy information

The modern decision-making environment is complex and dynamic. Global supply chain networks are increasingly exposed to unsystematic risks. Therefore, decision-makers need greater flexibility and precision to better manage uncertain market changes and complex international environments. To construct an accurate multi-criteria group decision-making (MCGDM) model, it is necessary to select appropriate evaluation criteria and identify alternative ranking methods based on specific decision problems. To develop a suitable MCGDM model for dynamic environments, this paper develops a new MCGDM model based on probabilistic interval-valued intuitionistic hesitant fuzzy sets (PIVIHFSs), regret theory, and the extended ELimination Et Choice Translating Reality (ELECTRE) III method. Firstly, this paper proposes two new aggregation operators, including the generalized probabilistic interval-valued intuitionistic hesitant fuzzy weighted averaging (GPIVIHFWA) operator and the generalized probabilistic interval-valued intuitionistic hesitant fuzzy weighted geometric (GPIVIHFWG) operator. To incorporate the decision-maker (DM)'s regret aversion, a bidirectional projection measure is proposed to calculate the advantages and disadvantages between two probabilistic interval-valued intuitionistic hesitant fuzzy elements (PIVIHFEs). The regret values of PIVIHFEs are determined using the bidirectional projection measure instead of utility values in the regret-rejoice function. Then, this paper constructs an extended ELECTRE III method and establishes a decision-making model based on the Borda rule for ranking and selecting the best alternatives. Finally, the effectiveness and robustness of the proposed model are verified through a numerical example, and the results are discussed through sensitivity analysis and comparative analysis.