A Natural Method for Ranking Objects from Hesitant Fuzzy Preference Relations

Abstract

Hesitant fuzzy preference relations (HFPRs) are efficient tools to denoting the decision maker’s judgements that permit the decision makers to compare objects using several values in [0, 1], and the number of elements in different hesitant fuzzy elements may be different. After reviewing the previous researches about decision making with HFPRs, one can find that there are several limitations. To avoid these issues and to guarantee the reasonable ranking order, this paper introduces a new additive consistency concept for HFPRs. Different from the previous consistency concepts, the new concept neither needs to add values into hesitant fuzzy elements nor disregards any information offered by the decision makers. To measure the additive consistency of HFPRs, two 0-1 mixed programming models are constructed. Meanwhile, an additive consistency based 0-1 mixed programming model is established to determining the missing values in incomplete HFPRs that can address the situation where ignored objects exist. Then, an algorithm to obtaining the hesitant fuzzy priority weight vector from (incomplete) HFPRs is provided. Considering group decision making, a new group consensus index is defined, and an interactive approach to improving the group consensus level of individual HFPRs is offered. Furthermore, a probability distance measure between two HFPRs is defined to deriving the weights of the decision makers. According to the additive consistency and consensus analysis, an approach to group decision making with incomplete and inconsistent HFPRs is performed. Finally, two practical numerical examples are provided, and comparison analysis is offered.