Consensus Model Driven by Interpretable Rules in Large-Scale Group Decision Making With Optimal Allocation of Information Granularity

In group decision making (GDM), consensus level is regarded as a critical criterion to measure the effectiveness and availability of the final group decision solution. Consensus model is aimed at conducting the decision group to reach agreement through the process of group negotiation, advice feedback, and opinion modification, which is time-consuming and rests with the willingness and behavior of individual decision makers. Thus, to guide the shift in the opinions of decision makers within a limited time, it is essential to design an effective, interpretable, and fair consensus mechanism in GDM, which is particularly vital when a mass of decision makers (e.g., more than 30) are involved in the decision process, viz., we encounter a large-scale GDM (LSGDM). With the involvement of information granulation, this study presents a rule-based consensus model in LSGDM by optimally allocating the level of information granularity to each decision maker. The opinions of decision makers in LSGDM are divided into different clusters by engaging the fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> -means method. Inspired by a generic fuzzy rule-based model, the radius of the individual preference granule (PG) is calculated by a weighted linear combination of the granularity levels allocated to the clusters. Then, a consensus model with the optimal allocation of information granularity (CMOIG) is built to determine the granularity level for each cluster by minimizing the sum of radii of individual PG. An interactive consensus reaching process is proposed with the proposed CMOIG and fuzzy modification rules. The CMOIG and fuzzy modification rules simultaneously guarantees high efficiency and interpretability, and the generation method of PGs leads to high fairness due to low discrepancy among the decision group. Finally, numerical and comparative experiments are conducted in detail to verify the validity and superiority of the presented models in terms of the efficiency, interpretability, and fairness.