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.

Probabilistic interval ordering, as a helpful tool for expressing positive and negative information, can effectively address multi-attribute decision-making (MADM) problems in reality. However, when dealing with a significant number of decision-makers and decision attributes, the priority relationships between different attributes and their relative importance are often neglected, resulting in deviations in decision outcomes. Therefore, this paper combines probability interval ordering, the prioritized aggregation (PA) operator, and the Gauss–Legendre algorithm to address the MADM problem with prioritized attributes. First, considering the significance of interval priority ordering and the distribution characteristics of attribute priority, the paper introduces probability interval ordering elements that incorporate attribute priority, and it proposes the probabilistic interval ordering prioritized averaging (PIOPA) operator. Then, the probabilistic interval ordering Gauss–Legendre prioritized averaging operator (PIOGPA) is defined based on the Gauss–Legendre algorithm, and various excellent properties of this operator are explored. This operator considers the priority relationships between attributes and their importance level, making it more capable of handling uncertainty. Finally, a new MADM method is constructed based on the PIOGPA operator using probability intervals and employs the arithmetic–geometric mean (AGM) algorithm to compute the weight of each attribute. The feasibility and soundness of the proposed method are confirmed through a numerical example and comparative analysis. The MADM method introduced in this paper assigns higher weights to higher-priority attributes to establish fixed attribute weights, and it reduces the impact of other attributes on decision-making results. It also utilizes the Gauss AGM algorithm to streamline the computational complexity and enhance the decision-making effectiveness.