A quantum group decision-making model for patient-capital project selection integrating cumulative prospect theory under linear Diophantine fuzzy uncertainty

The effective selection of patient-capital projects is crucial for promoting China’s transition toward low-carbon development, technological innovation, and sustainable value creation. However, such decision-making processes typically involve multiple experts whose assessments are affected by individual risk preferences and inter-expert opinion interference—factors that are seldom modeled simultaneously yet jointly exert significant influence in existing studies. To address these limitations, this study develops an integrated multi-criteria quantum group decision-making framework for patient-capital project selection, which combines linear Diophantine fuzzy sets (LDFSs), cumulative prospect theory (CPT), quantum probability theory (QPT), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). First, a linear Diophantine fuzzy Deng entropy (LDFDE) method is proposed to characterize the information uncertainty inherent in LDFSs. Second, a personalized criterion-weighting approach that integrates LDFDE with the classical entropy weighting method is developed to reflect both objective data variability and subjective expert preferences. Third, an integrated quantum CPT-TOPSIS model is constructed, in which the CPT-TOPSIS component captures behavioral biases and risk attitudes, while the QPT-based aggregation component models opinion interference to achieve more consistent and robust group decisions. Finally, a real-world case study on patient-capital project selection demonstrates the practicality and effectiveness of the proposed framework. We also report sensitivity and comparative analyses to validate that the proposed approach enhances ranking stability and reliability. In summary, the findings underscore the potential of the model as a reliable decision-support tool for complex, uncertain, and psychologically driven investment scenarios.