Multiple-attribute decision-making method based on the correlation coefficient between dual hesitant fuzzy linguistic term sets

Hesitant fuzzy linguistic term sets (HFLTS) and dual hesitant fuzzy sets (DHFS) are two important branches of fuzzy mathematics, both of which have been widely applied in multiple-attribute decision-making (MADM) problems under uncertain environments. To humanize the decision-making process, the former deals with hesitant fuzzy linguistic terms in line with people's common sense, and to reflect the nature of people's hesitancy, the latter deals with both the membership and nonmembership hesitancy functions of fuzzy sets (FS). However, as the decision-making environment is increasingly complex, the characteristics of these two sets need to be combined to more precisely represent the fuzzy linguistic information. Therefore, this paper proposes a new extension of the HFLTS concept, i.e., dual hesitant fuzzy linguistic term set (DHFLTS), to highlight the importance of the nonmembership degree for HFLTSs. Some properties for the DHFLTS are given. Motivated by information energy, the information energy for DHFLTS and the correlation coefficient between DHFLTSs as well as the weighted correlation coefficient are defined. Finally, a supplier selection problem is given to demonstrate the feasibility and superiority of this method.