Error Analysis Methods for Group Decision Making Based on Hesitant Fuzzy Preference Relation

Hesitant fuzzy preference relation (HFPR) is an effective way to depict the decision makers’ preferences over the objects (alternatives or attributes) in the process of group decision making. Each component of the HFPR is characterized by several possible values and can express the decision makers’ hesitant information comprehensively. To make a decision with the HFPR, it is very necessary to find a proper technique for deriving the priority weights from the HFPR. In this paper, we use the error analysis as a tool to develop several straightforward methods for the priorities of the HFPR. We first define the expected value and the average value of each hesitant fuzzy element in the HFPR. Then based on the error analysis, we come up with the interval midpoint method, the average value method, and the difference method to derive the priority weights from the HFPR. After that, we discuss the relations among these methods, and utilize them and the possibility degree formula to develop an approach to decision making with the HFPR. Finally, we demonstrate the effectiveness and practicality of our approach through a case study concerning the investment problem in liquor enterprise.