In recent years, the consensus-reaching process of large group decision making has attracted much attention in the research society, especially in emergency environment area. However, the decision information is always limited and inaccurate. The trust relationship among decision makers has been proven to exert important impacts on group consensus. In this study, we proposed a novel uncertain linguistic cloud similarity method based on trust update and the opinion interaction mechanism. Firstly, we transformed the linguistic preferences into clouds and used cloud similarity to divide large-scale decision makers into several groups. Secondly, an improved PageRank algorithm based on the trust relationship was developed to calculate the weights of decision makers. A combined weighting method considering the similarity and group size was also presented to calculate the weights of groups. Thirdly, a trust updating mechanism based on cloud similarity, consensus level, and cooperation willingness was developed to speed up the consensus-reaching process, and an opinion interaction mechanism was constructed to measure the consensus level of decision makers. Finally, a numerical experiment effectively illustrated the feasibility of the proposed method. The proposed method was proven to maximally retain the randomness and fuzziness of the decision information during a consensus-reaching process with fast convergent speed and good practicality.

Achieving consensus in group decision-making is both essential and challenging, especially in which non-cooperative behaviors can significantly hinder the process under uncertainty. These behaviors may distort consensus outcomes, leading to increased costs and reduced efficiency. To address this issue, this study proposes a data-driven robust minimum-cost consensus model (MCCM) that accounts for non-cooperative behaviors by leveraging individual adjustment willingness. The model introduces an adjustment willingness function to identify non-cooperative participants during the consensus-reached process (CRP). To handle uncertainty in unit consensus costs, Principal Component Analysis (PCA) and Kernel Density Estimation (KDE) are employed to construct data-driven uncertainty sets. A robust optimization framework is then used to minimize the worst-case consensus cost within these sets, improving the model’s adaptability and reducing the risk of suboptimal decisions. To enhance computational tractability, the model is reformulated into a linear equivalent using the duality theory. Experimental results from a case study on house demolition compensation negotiations in Guiyang demonstrate the model’s effectiveness in identifying and mitigating non-cooperative behaviors. The proposed approach significantly improves consensus efficiency and consistency, while the data-driven robust strategy offers greater flexibility than traditional robust optimization methods. These findings suggest that the model is well-suited for complex real-world group decision-making scenarios under uncertainty.

To address challenges in complex group decision-making (GDM)—specifically preference fuzziness, intricate subgroup segmentation, and non-cooperative behavior—this study proposes an adaptive consensus model based on probabilistic linguistic term sets (PLTSs). By integrating fuzzy C-means (FCM) clustering with a Gaussian mixture model (GMM), a fuzzy Gaussian mixture model (FGMM) is constructed to achieve soft segmentation of expert preference distributions. On this basis, an adaptive consensus feedback mechanism is developed, which dynamically integrates interactive and automated adjustment strategies via multi-level consensus thresholds, thereby balancing decision efficiency and quality. To identify and control non-cooperative behaviors, a cooperation index and a three-tier management strategy, which incorporates intra-group negotiation, weight penalties and an exit-delegation mechanism, were introduced. In the case of strategic decision-making of new energy vehicles (NEV), after four rounds of feedback iterations, the group consensus level increased from the initial 0.316 to 0.804, reaching the preset threshold and verifying the effectiveness of the consensus mechanism. Compared with the existing literature methods, the framework in this paper achieves more comprehensive integration and innovation in four aspects: preference expression, clustering mechanism, consensus feedback and behavior management.