Evaluating Green–Digital Transformation in Chinese Listed Firms: An LLM-Assisted Multi-Criteria and Graph-Learning Framework

Green–digital transformation has become a strategic priority for enterprises and policymakers, yet existing evaluation methods struggle to address criterion-weight uncertainty, relational dependencies among criteria and firms, and cross-firm heterogeneity. This study proposes a probabilistic uncertain linguistic best–worst method-intelligent decision-making framework integrating graph models and large language models (PUL-BWM-ID-GMLM). Large language models (LLMs) assist in eliciting criterion preference relations, which are converted into weights using the BWM with PUL term sets. Indicator-relationship and alternative-relationship graphs are then constructed and processed with graph neural networks (GNNs) to incorporate data-driven relational information among criteria and firms. The framework combines transformation indicators with organizational and regional conditions for multidimensional assessment. Applied to Chinese listed firms (2009–2021), the framework reveals temporal, industrial, and regional heterogeneity, with notable shifts in 2015, 2016, and 2019. Comparisons with six established multi-criteria decision-making methods reveal ranking differences, while ablation, robustness, and sensitivity analyses characterize component contributions and result stability. It offers a relationship-informed decision-support tool for comparing transformation development across firms, industries, and regions.