New distance measures of hesitant fuzzy linguistic term sets

Abstract Hesitant fuzzy linguistic term sets (HFLTSs) is an important decision-making tool for qualitative evaluation, and the distance measures between HFLTSs have been widely concerned. The purpose of this paper is to overcome the defects of the existing distance measures between HFLTSs and propose some improved and more reasonable distance measures of HFLTSs. Firstly, we find that the existing HFLTSs distance measures do not satisfy basic properties such as triangle inequality through analysis. Additionally, considering that the existing distance measures do not think about the influence of the different number of linguistic terms on the calculated results, some distance measures considering both the decision-makers’ hesitance degree and linguistic term values are further proposed. The developed distance measures not only satisfy the basic properties but also avoid the loss of decision information. Finally, the developed distance measures are applied to the field of judicial execution and compared with the calculation results of the existing distance measures. The results show that the developed distance measures are more consistent with the actual decision-making process, which is helpful in improving the quality of decision-making.