A Robust Maximum Fairness Consensus Model With Limited Cost Under the Uncertain Trust Relationships and Individual Weights

The uncertainty of the trust relationships between decision makers (DMs) or the uncertainty of individual weights will lead to the uncertainty of fairness and consensus management in group. To provide a solid solution, we propose a robust maximum fairness consensus model with limited cost under the uncertain trust relationships and individual weights (RTRMFCM). Specifically, this article constructs an uncertainty set to more precisely describe the uncertainty of the trust relationship between DMs. Based on individual fair preference considerations from the trust network, we adopt a robust optimization method to reduce the risk of DMs feeling unfair. Furthermore, a robust approach based on the combination of uncertain individual weights has been developed to reduce the risk of consensus being destroyed. Then, some theoretical analyzes are presented. We also provide a numerical analysis to validate the applicability of the RTRMFCM. Finally, the simulation analyses have revealed the characteristics of the RTRMFCM, and show that the RTRMFCM is more effective than the maximum fairness consensus model with limited cost under trust relationship (TRMFCM).