Group Decision-Making Model With Hesitant Multiplicative Preference Relations Based on Regression Method and Feedback Mechanism

The hesitant multiplicative preference relation (HMPR) was initially put forward in 2013. Utilizing the HMPR, the decision makers can give some possible preference values from the Saaty's 1-9 scale for pairwise comparisons over alternatives. However, until now, there is little research on the consistency and consensus of HMPRs. In this paper, we focus on exploiting the regression method and the feedback mechanism to improve the consistency and consensus for HMPRs and developing an efficient group decision-making model with HMPRs. First, a regression method based on complete consistency is developed to reduce HMPRs to multiplicative preference relations (MPRs). After that, a novel consistency checking and revising method based on the threshold estimation method and the feedback mechanism is given to improve the consistency level of the reduced MPRs. Then, a group consensus index is put forward to calculate the deviation degree between the reduced MPR and the group MPR and it is utilized to develop a consensus reaching process based on the feedback mechanism to improve the group consensus level of the reduced MPRs. Next, a complete group decision-making model with HMPRs is developed to rank all the alternatives and select the best one. Finally, a numerical example with respect to the investment of shared bikes is presented to demonstrate the proposed group decision-making model and then we also compare our proposed model with the existing one.