A rational incentive mechanism driven group consensus optimization model by trust attenuation propagation with optimal path under social network

Traditional consensus feedback mechanisms often rely on established models, assuming that trust is transmitted without loss among decision makers and that consensus is achieved solely based on this ideal process. However, they fail to consider trust attenuation due to path differences during propagation and the varying tolerance of decision makers towards opinion adjustments. To address this issue, this paper proposes a group consensus optimization model driven by a rational incentive mechanism, integrating trust attenuation propagation with optimal trust path selection. First, an inverse dynamic programming model with trust amplitude is developed to explore the optimal propagation path of trust relationships between decision makers. Second, a distributed linguistic trust propagation operator considering trust attenuation (impacts of path length and decision makers' positions in the trust chain) is constructed to analyze the dynamic changes of trust relationships during propagation. Furthermore, a dynamic incentive feedback model based on rational adjustment is established, followed by a minimum adjustment optimization model driven by the rational incentive mechanism. The key innovation of the model lies in: enhancing decision makers' willingness to adjust opinions proactively through incentives (avoiding resistance from forced adjustment) and constraining rational adjustment within a maximum tolerance range (mitigating divergence caused by trust transmission risks). Finally, a case study of builder selection for industrial park construction illustrates the effectiveness and superiority of the proposed method.