A group stability-based consensus model for multi-criteria group decision-making problems with linguistic distribution assessments

In multi-criteria group decision-making (MCGDM) problems with linguistic distribution assessments (LDAs), this study proposes a group stability-based consensus model to facilitate the generation of solutions that satisfy predefined group stability and group consensus requirements. The group stability and group consensus measures are constructed at the criteria, alternative, expert, and global levels. In terms of different degrees of group stability and group consensus in MCGDM problems, it can be categorized into four situations by comparing with predefined thresholds, which are: 1) group stability measure is satisfied, and group consensus measure is satisfied; 2) group stability measure is not satisfied, and group consensus measure is satisfied; 3) group stability measure is satisfied, and group consensus measure is not satisfied; 4) group stability measure is not satisfied, and group consensus measure is not satisfied. To accelerate the group stability-based group consensus reaching process, optimization problems with group stability and group consensus requirements are constructed to obtain suggested intervals and recommended intervals for LDAs. This contributes to the feedback mechanisms corresponding to the four different situations. The proposed method is applied to an ultrasonic medical imaging workstation selection problem to demonstrate its effectiveness. The superiority of the proposed method is validated through comparative experiments.