Hesitancy degree-based correlation measures for hesitant fuzzy linguistic term sets and their applications in multiple criteria decision making.

The hesitant fuzzy linguistic term set (HFLTS) turns out to be useful in representing people's hesitant qualitative information. The aim of this paper is to investigate new correlation measures between HFLTSs and apply them in decision-making process. Firstly, the concepts of mean and hesitancy degree of hesitant fuzzy linguistic elements are introduced. Based on them, we address the drawbacks of the existing correlation measures between HFLTSs. Then, a new correlation coefficient between HFLTSs is established. Additionally, the hesitancy degree of the hesitant fuzzy linguistic correlation coefficient is proposed, which is composed by the upper and lower bounds of the hesitant fuzzy linguistic correlation coefficient. To show the applicability of the proposed correlation measures, a correlation coefficient-based method is developed for multiple criteria decision making in the cases that the weights of criteria are either known or unknown. A practical example concerning the strategic management of Sichuan liquor brands in China is given to validate the proposed method. It is verified that the proposed correlation coefficients between HFLTSs is more convincing than the existing ones and the developed correlation coefficient-based hesitant fuzzy linguistic MCDM with the weights of criteria being either completely known or unknown is applicable.