A two-stage consensus reaching model for group decision making with reciprocal fuzzy preference relations

Reciprocal fuzzy preference relation (FPR) is a hot topic in the research field of group decision making (GDM). Within the framework of GDM, a two-stage consensus reaching model is proposed to modify the decision makers' (DMs') FPRs. In the first stage which is called consistency improving stage, a consistency index and an iterative algorithm are employed to measure and improve individual consistency, respectively. In each iteration of the algorithm, only one pair of preference values, which deviates the most from the corresponding elements in the consistent FPR matrix, are modified to keep the DM's original information as much as possible. In the second stage which is called consensus reaching stage, individual consensus index and group consensus index are applied to measure consensus. A convex quadratic programming model is developed to help DMs reach consensus. Some desired properties of the model are also investigated and testified. What's more, the final individual consistency is also limited to an acceptable threshold. Finally, a practical example is used to illustrate the validity of the proposed consensus model.