Research on a Social Network Group Decision-Making Method for Incomplete Probabilistic Linguistic Information

In social network group decision-making (SN-GDM), decision-makers usually employ probabilistic linguistic term sets (PLTSs) to express vague and hesitant evaluation information. However, owing to cognitive limitations, incomplete information, and the complexity of social trust relationships, the probabilistic linguistic assessments provided by decision-makers are often incomplete, which reduces the reliability of group evaluation aggregation and increases the difficulty and cost of consensus reaching. To address this issue, this paper proposes a social network group decision-making method for incomplete probabilistic linguistic information. First, a confidence level for each evaluation position is constructed by integrating social trust relationships and the certainty of evaluation information, and incomplete PLTSs are estimated on the basis of the DeGroot model so as to improve the completeness and reliability of individual decision matrices. Second, the comprehensive certainty of evaluation information and the individual-group average similarity are fused, and the Einstein t-norm is used to determine decision-maker weights; on this basis, a group decision matrix and multi-level consensus measures at the evaluation-position, decision-maker, and group levels are established. Furthermore, when group consensus fails to reach a preset threshold, regret theory is introduced to characterize the psychological adjustment pressure generated when decision-makers deviate from group opinion, and, together with confidence levels and information from trusted neighbors, a personalized consensus reaching mechanism containing identification and modification rules is constructed. Finally, the proposed method is validated through a case study on the selection of investment directions for Guangxi’s low-altitude economy.