Approach for Dual Probabilistic Linguistic Decision-Making Under Unknown Attribute Weights Based on Archimedean Power Muirhead Mean Operators

Dual probabilistic linguistic term sets (DPLTSs) provide a powerful tool for describing uncertain, hesitant, and bipolar linguistic assessments in complex decision-making settings. Current aggregation methods for dual probabilistic linguistic information still have drawbacks. They can hardly mitigate the interference brought by biased assessment values and fail to capture the correlations among arbitrary attributes. To address these limitations, this paper develops a new class of dual probabilistic linguistic Archimedean power Muirhead mean (DPLAPMM) operators for multipleattribute decision making (MADM). First, by combining the advantages of Archimedean triangular norms with the power Muirhead mean (PMM) operator, the DPLAPMM operator together with its weighted form are developed. The proposed operators can reduce the impact of unreasonable evaluation values while modeling the interrelationships among any number of attributes. Then, a dual probabilistic linguistic entropy is constructed to obtain objective attribute weights, which are combined with subjective weights to generate comprehensive attribute weights. Based on these results, a MADM method is established under a dual probabilistic linguistic environment. An illustrative case concerning industrial artificial intelligence (AI) project selection is used to demonstrate the applicability of the proposed method, and comparative analyses show its flexibility and effectiveness over existing approaches.