An Improved Laplacian Gravity Centrality-Based Consensus Method for Social Network Group Decision-Making with Incomplete ELICIT Information

With the advancement of information technology, social media has become increasingly prevalent. The complex networks of social relationships among decision-makers (DMs) have given rise to the problem of social network group decision-making (SNGDM), which has garnered considerable attention in recent years. However, most existing consensus-reaching methods in SNGDM only consider local network information when determining the influence of DMs within the social network. This approach fails to adequately reflect the crucial role of key DMs in regulating information propagation during the consensus-reaching process. Additionally, the partial absence of linguistic evaluations in the decision-making problems also poses obstacles to identifying the optimal alternative. Therefore, this paper proposes an improved Laplacian gravity centrality-based consensus method that can effectively handle incomplete decision information in social network environments. First, the extended comparative linguistic expressions with symbolic translation (ELICIT) are utilized to describe DMs’ linguistic evaluations and construct the incomplete decision matrix. Second, the improved Laplacian gravity centrality (ILGC) is proposed to quantify the influence of DMs in the social network by considering local and global topological structures. Based on the ILGC measure, we develop a trust-driven consensus-reaching model to enhance group consensus, which can better simulate opinion interactions in real-world situations. Lastly, we apply the proposed method to a smart city evaluation problem. The results show that our method can more reasonably handle incomplete linguistic evaluations, more comprehensively capture the influence of DMs, and more effectively improve group consensus.