Abstract
•This paper offers a GDM method with DHFPEs.•The proposed method can deal with inconsistent and incomplete DHFPEs.•It calculates the priority vector following the consistency analysis.•It considers consensus and builds model for reaching the consensus requirement.•The application and comparison is offered by using a practical problem.
Considering the advantages of dual hesitant fuzzy elements (DHFEs) for describing the hesitant and intuitionistic judgments of experts and identifying the limitations of previous research about dual hesitant fuzzy decision making, this paper studies decision making with dual hesitant fuzzy preference relations (DHFPRs) and provides a new group decision making (GDM) method based on a series of built optimization models. A multiplicative consistency concept for DHFPRs is first introduced and analyzed. On the basis of this concept, optimization describing the multiplicative consistency of DHFPRs is realized. Meanwhile, stepwise optimization models for obtaining complete multiplicatively consistent DHFPRs are constructed, and a method for calculating the intuitionistic fuzzy priority vector is offered. Then, optimization models for determining unknown values in incomplete DHFPRs are formed in view of the multiplicative consistency. An index for measuring the consensus is defined and optimization models for reaching the consensus requirement of a group are established. Furthermore, consensus-based optimization models for determining the weights of experts are established. In view of the multiplicative consistency and consensus analysis, a detailed procedure for GDM with incomplete and inconsistent DHFPRs is provided. Finally, the new method is illustrated by a case study concerning an evaluation of the environmental performance of enterprises and associated comparative analyses are reported.