Abstract: In social network group decision-making, decision makers rely on social relationships and interactions to achieve collective decisions. Social relationships are crucial in this process as they not only serve as channels for information exchange but also influence the opinions and behaviors of the members. Furthermore, strong social relationships foster trust and cooperation among decision makers, thereby enhancing the efficiency of the decision-making process and increasing the acceptability of the outcomes. Therefore, many studies have focused on the exploration of the unknown social relationships to obtain a relatively complete social network, aiming at providing a powerful tool for analyzing individual interactions. But they have failed to adequately capture the randomness and uncertainty of decision makers’ social behaviors as they believe that a connection can be established between any two decision makers as long as there is an accessible path. Additionally, in the social network group decision-making, decision makers finally reach a consensus, or have opinions of polarization or divide after discussion and consultation. This is a dynamic process accompanied by the emergence of new opinions and the establishment of new social relationships. Differences in opinion among decision makers are inevitable due to the potential conflicts of interests. Consequently, some consensus decision-making models based on social relationships have been proposed, but they do not effectively model the potential interactions between decision makers. They also ignore the fact that the establishment of social relationships and opinion adjustments are a parallel process in actual decision-making. Given the above, it is necessary to propose a new social network group decision-making model. It includes a new social network completeness analysis method and opinion adjustment process to fully leverage the role of social relationships and potential individual interactions in promoting consensus.
Existing research on social network group decision-making lacks the analysis of decision-makers’ social paradigms. Additionally, current consensus adjustment processes fail to capture potential interactions between decision-makers and strangers. To address both issues, this paper proposes a consensus decision-making model based on social link probability and group selection. It guides decision makers with conflict opinions to communicate effectively based on analyzing the mutual influence between social relationship establishment and opinion adjustment, so as to eliminate opinion difference and promote consensus. The main contributions are as follows. First, the social link probability is used to quantify the probability of decision makers establishing social relationship through direct or indirect interactions, capturing the uncertainty and dynamics of social network. The concept of social link probability is derived from the link prediction in network science, which aims to predict the probability of forming connections between unlinked nodes based on known node and network structure. Then an integrated rule for social link probability is proposed, considering the choice of social paradigms to estimate the probability of forming new social relationships between decision makers. Second, a multi-objective consensus feedback model based on social link probability is developed for maximizing social link probability and prioritizing the resolution of opinion differences. The results are used to update the social network and adjust the opinions of conflicting individuals, thereby enhancing group consensus.
The feasibility and applicability of the model are demonstrated through a numerical example. This paper compares the model with existing consensus adjustment models, providing a detailed analysis of its performance. The comparison highlights the rationality and advantages of the proposed model from the range of final opinions, required adjustment rounds, the number of individuals with modified opinions, total adjustment degree and the process of the social network analysis. A series of simulation experiments are conducted to verify the stability and superiority of the model. The results indicate that the model not only achieves good consensus convergence but also has a superior ability to adapt to social networks with varying densities. This adaptability is crucial as it results in a higher rate for consensus achievement, making the model highly effective in diverse scenarios.

Key words: social network group decision-making, social paradigm, social link probability, opinion interaction, multi-objective consensus feedback model

摘要： 针对现有社会网络群体决策研究中缺乏对决策个体社交方式的综合分析,以及共识调整过程不能有效利用决策个体之间潜在互动等问题,本文提出基于社交链接概率与群体选择的共识决策模型。首先,使用社交链接概率反映决策个体在特定环境和约束条件下与他人互动,进而建立社会关系的倾向,而后提出同时考虑直接和间接社交方式的社交链接概率计算方法,以量化决策个体之间形成新社会关系的可能性。其次,为冲突个体制定考虑潜在社交对象的意见交互规则,并构建基于社交链接概率的多目标共识反馈模型,用于缓解冲突个体的意见分歧,优化社会网络结构并提高群体共识水平。最后,通过数值算例演示所提模型的可行性和适用性,并通过对比分析和仿真实验验证所提模型的有效性和优势。

关键词: 社会网络群体决策, 社交方式, 社交链接概率, 意见交互, 多目标共识反馈模型