Consensus evolution networks: A consensus reaching tool for managing consensus thresholds in group decision making

The consensus reaching process (CRP) is a critical part of group decision making (GDM). In order to explore the evolution of consensus, a new CRP tool is proposed based on consensus evolution networks (CENs). The CENs are built based on the consensus degrees among decision makers (DMs) and allow us to manage the consensus thresholds and its evolution. A new consensus index is introduced based on the structured and numerical aspects of the CENs. The new consensus index can not only deeply analyze the constitution of consensus, but also determine the weights of DMs. According to the clustering coefficient, the sensitive consensus threshold is identified and the sensitive consensus evolution network (SCEN) is built. Based on the complementary SCEN, a pairwise feedback adjustment method is proposed to improve consensus. Besides, the sparsity of the CENs can act as a reference to determine the agreed consensus thresholds, which is considered an important issue in traditional models. A numerical example is used to verify the usefulness of the proposed CRP tool. The numerical results show that the evolution of consensus can be clearly found based on CENs and the pairwise method can improve consensus in only four rounds.