Dynamic Trust Networks Based on Correlative-Z-Number: A Consensus Model Under Dual Feedback Mechanism

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With the rapid development of social media, social network group decision-making (SNGDM) has gained significant attention for its ability to integrate decision-makers' (DMs) social relationships. However, existing consensus models face challenges in dynamic trust evolution, single-dimensional consensus evaluation, and information integrity, making it difficult to address decision-making needs in complex uncertain environments effectively. To overcome these limitations, this study proposes a consensus model based on Correlative-Z-numbers (Cor-Z-numbers) and a dual-feedback mechanism to enhance the reliability and adaptability of group decision-making. First, Cor-Z-number is introduced, integrating Set Pair Analysis (SPA) to incorporate fuzziness and reliability information. A complete trust network and a dynamic trust network are constructed to simulate trust evolution and opinion interaction, leading to the development of an Intrinsic Adaptive Regulation Mechanism (IARM). Second, a dual-layer consensus framework is established, combining ordinal and cardinal consensus rules to improve consensus assessment. To optimize opinion adjustments, an Extrinsic Triggered Modified Mechanism (ETMM) is proposed, consisting of a minimal adjustment model and a minimum-cost adjustment increment model, ensuring a balance between consensus optimization and information preservation. Finally, a case study validates the effectiveness and superiority of the proposed model. Experimental results demonstrate its significant advantages in handling decision-making uncertainty, improving consensus efficiency, and reducing adjustment. In the Hengshui environmental governance case, the model effectively optimized consensus while preserving decision information, highlighting its practical value for complex environmental management.