As real-world decision-making increasingly involves complex and vague information under uncertain circumstances, the q-rung orthopair probabilistic hesitant fuzzy set (q-ROPHFS) has emerged as a significant generalization of conventional fuzzy sets, offering enhanced capability in managing uncertainty. Meanwhile, the combined compromise solution (CoCoSo) method, which synthesizes multiple decision-making strategies from a compromise perspective, is recognized as a powerful technique in multi-attribute decision-making (MADM). In this context, this paper develops a novel MADM framework that integrates the CoCoSo method with q-ROPHFSs. To begin with, by extending the Frank t-norm and t-conorm to q-ROPHFSs, a series of q-ROPHF Frank aggregation operators are proposed, including several weighted forms of q-ROPHF Frank average and geometric operators. Their desirable properties are also systematically examined. Subsequently, subjective weights derived from the modified best–worst method (BWM) and objective weights obtained via the entropy weight method are combined to construct a BWM–entropy-based integrated weighting model within the q-ROPHFS context. Based on the proposed aggregation operators and the combined weighting model, an integrated BWM–entropy–CoCoSo decision-making framework is developed to support MADM under q-ROPHFS environments. Finally, the applicability and practicality of the proposed method are demonstrated through a case study on renewable energy project selection. Its reliability and robustness are further validated through sensitivity analysis of key parameters. In addition, the advantages of the integrated MADM framework are confirmed via a comparative analysis with existing approaches.
Ruan et al. (Wed,) studied this question.