Heterogeneous Hesitant Fuzzy Preference Relation and Its Application in Group Decision-making

When dealing with group decision making problems, preference relations can give full play to the subjective initiative of decision makers and quantify uncertain information into numerical or linguistic levels, thus reducing the decision-making error caused by subjective assumptions. Considering that the hesitant preference relationship can more comprehensively represent the preference information of decision makers, we study the heterogeneous hesitant fuzzy preference relationship of confidence and apply it to group decision-making problems. Firstly, the consistency of three hesitant preference relationships is defined, and three optimization models are established to obtain the weight vector of alternatives. Secondly, the process of building group consensus is established, and feedback mechanisms are used to provide decision-makers with adjustment directions. By gradually adjusting preference relationships, satisfactory decision results and group consensus levels are achieved, and a group decision-making model is established. Finally, the effectiveness and feasibility of the model established in the article in complex decision-making environments were verified through specific examples and comparative analysis.