Marginal Contribution-Based Personalized Consensus Analysis for Interval Fuzzy Group Decision Making

Interval fuzzy preference relations (IFPRs) offer a concise and intuitive representation of the uncertain cognition of decision makers (DMs). Discussions on consistency and consensus are crucial in group decision-making with IFPRs. Consistency prevents self-contradictory judgments, while consensus restricts the disparities among DM assessments within a predetermined threshold. Both have a significant impact on decision quality. Hence, the Shapley consistency and consensus mechanism (SHAP-CCM), which endows the adjustment to DMs by considering their marginal contributions to the minimum total adjustments of all corresponding coalitions, is introduced. Under each DM’s Shapley consensus adjustment, personalized judgment adjustment strategies are considered due to DMs’ intrinsic characteristic differences. In rare scenarios where the Shapley value may fall below zero, this could result in other DMs bearing a greater adjustment. Thus, we propose the Nash-bargaining consensus adjustment based on max–min marginal contribution. This method effectively addresses the issue associated with SHAP-CCM, enhancing the reliability of the analysis. With these mechanisms, the corresponding group decision methods are given. Meanwhile, numerical and comparative discussions show the concrete application and superiority of the new results.