A group consensus reaching model balancing individual satisfaction and group fairness for distributed linguistic preference relations

In real-world complex group decision-making problems, preference inconsistency and opinion conflict are common and crucial challenges that need to be tackled. To promote consensus reaching, a novel group consensus reaching model is constructed considering individual satisfaction and group fairness. This study focuses on managing the group consensus reaching process based on flexible and adaptable information, modelled as distributed linguistic preference relations (DLPRs). First, a building process for DLPRs is discussed by integrating cumulative distribution functions converted from single linguistic term sets, hesitant fuzzy linguistic term sets, and comparative linguistic expressions. Furthermore, a two-stage consistency improvement method is proposed, which makes a trade-off between the frequency and magnitude of adjustments. Finally, we establish an improved group consensus model to balance individual satisfaction and group fairness, where individual satisfaction is measured by the deviation between the original and revised preferences and group fairness is measured by the deviation between individual satisfactions. The emergency response plan selection is conducted to show the validity and advantages of the proposed approach.