Higher-order interaction of stability simplicial complex driven group consensus reaching in social network

To group decision-making (GDM) under social network, the interactions are no longer limited to pairwise but can take higher-order interaction, which can affect the consensus process. The higher-order interaction can be represented in simplicial complex. Therefore, under social network, this paper deeply explores a new higher-order interaction-based adjustment model in the simplicial complex. Firstly, we identify simplicial complex by utilizing the consensual objective and subjective trust information, and determine the decision maker weights. Then, we design the stability of simplex from the system structure and select the adjustment alternative and decision maker to construct the adjustment model based on the consensus and the stability of simplex. Considering the simplex structure, inspired by spreading dynamics model of simplex, we propose strengthening mechanism and competing mechanism of higher-order evaluation interaction. Further, this paper establishes a higher-order interaction-based minimum adjustment model. Because of the connectedness of simplicial complex, decision makers between simplices may occur the spontaneous interaction. In this case, we construct a global stability of simplicial complex to improve the minimum adjustment model. Finally, we use an example to expound the feasibility of our method, and design also a comparative analysis to demonstrates its advantages. In general, our method can significantly improve the consensus level and changes the adjustment decision maker selection from the system structure.