<p>Probabilistic linguistic term sets provide a way to express decision-making information using linguistic terms, particularly making it widely used in decision-making. However, in traditional multi-attribute group decision-making (MAGDM), the computation of attribute weights is usually given directly or calculated from existing data, and the results obtained fail to consider the stochastic nature of attribute weights. In addition, when considering the irrational psychology of decision-makers (DMs), the attention of decision-making fairness is not enough. Therefore, this study addresses existing challenges in MAGDM by proposing a novel probabilistic linguistic MAGDM framework integrated with maximum likelihood estimation. Firstly, the intricacy of the decision-making process may lead to unfairness, then considering the fairness issue of DMs, we develop an approach to reach a consensus that combines fairness theory with minimum adjustment cost consensus model. Subsequently, we address the issue of attribute weights determination. To enhance the accuracy of this process, we treat weights as stochastic variables and optimize these weights through maximum likelihood estimation. Finally, for alternative prioritization, we combine grey relational analysis with fairness theory to identify the most suitable alternative. The effectiveness of the proposed method is confirmed through an empirical analysis on digital rural governance, while sensitivity analysis and comparative evaluations demonstrate its superiority in robustness and efficiency.</p>