Group decision making with compatibility measures of hesitant fuzzy linguistic preference relations

Compatibility measure is a very well-known method to deal with decision making problems with uncertain preference relations. In this paper, on the basis of generalized distance measure of hesitant fuzzy linguistic elements, we define the compatibility measures for hesitant fuzzy linguistic preference relations (HFLPRs), including compatibility degree, compatibility index, and acceptable compatibility, and some important special properties are also discussed. Furthermore, based on the compatibility measures of HFLPRs, we propose a method for determining the experts' weights in group decision making (GDM), as well as establish an algorithm for solving the GDM problem with HFLPRs. A case study is set up to utilize the compatibility measures of HFLPRs for dealing with a practical GDM problem, which is to determine which aspect is optimal in the process of medical and health system reform. Finally, some comparisons and analyses are also discussed in detail.