Cooperative Game-based Consensus Adjustment Mechanism with Distribution Linguistic Preference Relations for Group Decision Making

Distribution linguistic preference relations (DLPRs) play a crucial role in group decision making due to their ability to capture hesitation and uncertainty in individual judgments. By utilizing multiple linguistic variables with associated distribution proportions, DLPRs offer a flexible way to represent preferences. However, current models that use DLPRs often overlook two crucial factors: the ordinal consistency of preference relations and the fairness of adjustment allocation within the DLPRs-based consensus reaching process. In this paper, we propose a cooperative game-based minimum adjustment consensus reaching mechanism that accounts for both ordinal consistency and the hesitant degree in DLPRs. This approach leverages the properties of indices in cooperative game theory to ensures a fair allocation of consistency and consensus adjustments, while maintaining ordinal consistency and controlling the hesitant degree of DLPRs through the construction of appropriate constraints to preserve their quality. Additionally, a new algorithm is developed to manage completeness, ordinal and acceptable cardinal consistency, consensus-reaching, and hesitation in scenarios involving incomplete DLPRs. Finally, a case study is provided to demonstrate the practical application of the proposed method. Sensitivity and comparative analyses with existing models are performed to assess the performance of the approach in terms of quality, fairness, and efficiency.