A new approach for group decision making method with hesitant fuzzy preference relations

Abstract This paper focuses on group decision making with hesitant fuzzy preference relations (HFPRs). To derive the consistent ranking order, a new multiplicative consistency concept for HFPRs is introduced that considers all information offered by the decision makers. The main feature is that this concept neither adds values to hesitant fuzzy elements nor disregards any information provided by the decision makers. To judge the multiplicative consistency of HFPRs, 0–1 mixed programming models are constructed. According to the assumption that there is an independent uniform distribution on values in hesitant fuzzy elements, the hesitant fuzzy priority weight vector is derived from multiplicative consistent reciprocal preference relations and their probabilities. Meanwhile, several consistency based 0–1 mixed models to estimate missing values in incomplete HFPRs are constructed that can address the situation where ignored objects exist. Considering the consensus in group decision making, a distance measure based consensus index is defined, and a method for improving the group consensus is provided to address the situation where the consensus requirement is unsatisfied. Then, a distance measure between any two HFPRs is introduced that is used to define the weights of the decision makers. Furthermore, a multiplicative consistency and consensus based interactive algorithm for group decision making with HFPRs is developed. Finally, a multi-criteria group decision making problem with HFPRs is offered to show the concrete application of the procedure, and comparison analysis is also made.