A New Distance-Based Consensus Reaching Model for Multi-Attribute Group Decision-Making with Linguistic Distribution Assessments

This paper proposes a novel consensus reaching model for multi-attribute group decision making (MAGDM) with information represented by means of linguistic distribution assessments. Firstly, some drawbacks of the existing distance measures for linguistic distribution assessments are analyzed by using numerical counterexamples, and a new distance measure is proposed for linguistic distribution assessments in order to alleviate the limitations. Then, a novel consensus reaching model is developed for MAGDM with linguistic distribution assessment, in which a feedback mechanism is devised by combining an identification rule and an optimization-based model. In this consensus framework, the model allows experts who are identified to modify their preferences to provide additional preference information about linguistic distribution assessments in each iteration. Meanwhile, by solving an optimization model, the consensus reaching model can automatically generate preference adjustment suggestions for experts. Moreover, the optimization model solved in each iteration minimizes the deviation between the adjusted values and initial preferences, which in turn leads to the good performance of the proposed consensus reaching model in preserving the initial preference information. Finally, an illustrative example shows that the proposed consensus reaching model is feasible and effective, and a comparative analysis highlights the advantages and characteristics of the model.