Linguistic Dual Hesitant Fuzzy Preference Relations and Their Application in Group Decision-Making

Intuitionistic fuzzy preference relations (IFPRs) can not only deal with the uncertainty and vagueness of decision makers' judgments but also describe the information from the aspects of preferred and non-preferred, respectively. Thus, it has proved to be an efficient tool for solving group decision-making (GDM) problems. However, considering the expression of linguistic information of the current extended IFPRs is limited by a single linguistic term, it is still imperfect to deal with GDM problems. Hence, this paper first proposes a novel extended IFPRs as linguistic dual hesitant fuzzy preference relations (LDHFPRs) by utilizing a set of ordered linguistic terms to describe the preferred and non-preferred evaluation information, which recognize the uncertainty and hesitance of each decision maker and conform to real-life decision-making situations better. Subsequently, we construct the conditions of additive consistency and develop a maximum consistency linear programming model to cope with the problem of inconsistent LDHFPRs. Furthermore, a novel consensus reaching process which pays more attention to the minority but important individual opinions is established. Finally, a real-world application is utilized to demonstrate the effectiveness of the proposed method, and a comparison with the existing related works is presented to show the advantages and innovation of the proposed GDM method.