The consistency measures and priority weights of hesitant fuzzy linguistic preference relations

Hesitant fuzzy linguistic preference relations (HFLPRs) have already been widely used in decision making. It can deal with the situation that the decision makers (DMs) are hesitant in more than one linguistic term when giving the evaluation of the alternative. In order to obtain the consistent preference information, we propose a new definition of the consistency of HFLPRs in this paper, and simultaneously propose one consistency measure method based on the hesitant goal programming model. Based on the method, we can also derive priority weights from HFLPRs for ranking the alternatives. We further measure the HFLPR whether it satisfies the satisfactory consistency by using the consistency index of linguistic preference relations (LPRs), which is called Linguistic Geometric Consistency Index (LGCI). For those which are inconsistent, we propose a modeling optimization method and an iterative optimization method to improve them. Finally, an application example which demonstrates the different situations including the consistency, satisfactory consistency and consistency improvement based on the hot topic “sharing bike”, to show the practicability of the proposed methods And the comparisons with other methods are also used for revealing the advantages of our methods.