With the rise of social network group decision-making (SN-GDM), research on trust relationships has aided in achieving group consensus. However, as network structures grow more complex, there is a growing focus on studying overlapping communities. Most existing methods do not take into account the overlap between communities, thereby not fully revealing the interactive consensus within groups where many users are involved. Additionally, the role of overlapping nodes, which belong to multiple communities, in information exchange and promoting cooperation deserves further investigation. To address these issues, this research provides a maximum proximity-based feedback mechanism, utilizing overlapping structures, which offers effective and acceptable recommendations to guide subgroup interactions. First, higher order structural importance-based method (HoSIM) is used to detect overlapping communities, followed by the concept of proximity degree (PD) for the first time to identify high-quality overlapping nodes within them. Second, a feedback mechanism driven by overlapping communities based on proximity is proposed. By using PDs as weights, it participates in the formation of recommendations and the determination of interaction willingness, thereby improving the group consensus to the desired level. Finally, through numerical experiments and comparative analysis, the superiority of this study is demonstrated not only in consensus rounds but also in adjusting costs.

Trust relationships can facilitate cooperation in collective decisions. Using behavioral incentives via trust to encourage voluntary preference adjustments improves consensus through mutual agreement. This article aims to establish a trust incentive-driven framework for enabling consensus in social network group decision making (SN-GDM). First, a trust incentive mechanism is modeled via interactive trust functions that integrate risk attitude. The inclusion of risk attitude is crucial as it reflects the diverse ways decision makers (DMs) respond to uncertainty in trusting others’ judgments, capturing the varied behaviors of risky, neutral, and insurance DMs in the consensus process. Inconsistent DMs then adjust opinions in exchange for heightened trust. This mechanism enhances the importance degrees via a new weight assignment method, serving as a reward to motivate DMs to further align with the majority. Subsequently, a trust incentive-driven bounded maximum consensus model is proposed to optimize cooperation dynamics while preventing over-compensation of adjustments. Simulations and comparative analysis demonstrate the model’s efficacy in facilitating cooperation through tailored trust incentive mechanisms that account for these diverse risk preferences. Finally, the approach is applied to evaluate candidates for the Norden Shipping Scholarship, providing a cooperation-focused SN-GDM framework for achieving mutually agreeable solutions while acknowledging the impact of individual risk attitude on trust-based interactions.

This article proposes a decayed trust propagation method among multiple overlapping communities, and establishes a trust-driven consensus model for social network group decision making (SN-GDM). On the one hand, the use of overlapping nodes simplifies trust propagation by bridging complex connections among multiply overlapping communities. On the other hand, trust models' accuracy and realism are enhanced with the concept of trust decay, which accounts for the temporal dynamics of trust propagation. Thus, a first objective of this paper is to develop a trust propagation operator based on trust decay among multiple overlapping communities by leveraging overlapping nodes. By incorporating overlapping nodes' diverse trust relationships and perspectives, this approach allows to achieve reliable sources for generating recommendations in SN-GDM. A second objective of this paper is to design a decayed trust propagation induced consensus model to determine the optimal combination of overlapping nodes and feedback parameters, while balancing consensus efficiency and interaction willingness. The innovation of this approach is grounded in its ability to avoid excessive group adjustment to reach consensus. Numerical examples and comparative analysis demonstrate the model's performance in achieving efficient consensus under various representative recommendations.

Social network group decision-making (SN-GDM) provides valuable support for obtaining agreed decision results by effectively utilizing the connected social trust relationships among individuals. However, the impact of intricately overlapped social trust relationships within overlapping communities on evaluation modifications in the SN-GDM consensus reaching process is seldom considered. To alleviate this issue, this study attempts to construct an overlapping community driven feedback mechanism for improving consensus in SN-GDM. The Lancichinetti-Fortunato method (LFM) is used to detect the overlapping community structures under social trust networks. Subsequently, the trusted recommendation advice is conducted within overlapping communities, which guides the inconsistent subgroups to make an interaction with each other to reach higher consensus level. Then, an associated feedback mechanism for SN-GDM with overlapping communities is proposed, which enables the inconsistent subgroups to minimize the consensus cost by selecting personalized feedback parameters. Moreover, it shows that the overlapping communities based feedback mechanism is superior to the feedback mechanisms with non-overlapping communities. Finally, an illustrative example is included, which is also used to testify the efficacy of proposal by comparing the consensus cost under different representative recommendation advice in overlapping social trust networks.