An integrated method for multi-criteria decision-making based on the best-worst method and Dempster-Shafer evidence theory under double hierarchy hesitant fuzzy linguistic environment

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is a newly developed complex linguistic expression model, and has been well applied to multi-criteria decision-making (MCDM) problems. However, the determination of criteria weights and the innovation of decision-making methods are still two issues that worth exploring in this field. At present, conventional weight-determination methods sometimes have the disadvantages of complicated calculation and low consistency of the obtained results. On the other hand, the existing methods for linguistic information sometimes cannot consider the uncertainty of information caused by ignorance. Considering that the best-worst method (BWM) is a weight-determination method, which can not only greatly simplify the calculation process, but also improve the consistency degree of the results. Dempster-Shafer evidence theory (DSET) can better deal with information uncertainty caused by ignorance. Therefore, this paper extends the BWM and DSET to double hierarchy hesitant fuzzy linguistic environment to solve the above two problems respectively, and the DHHFL-BWM-DSET method is proposed. First, the weight of each criterion is derived based on the BWM-based weight-determination method. Then, inspired by DSET, we propose a DSET-based MCDM method which can not only obtain the decision results of a single decision maker, but also integrate the decision information of multiple decision makers to obtain more rational results. Therefore, decision makers can choose the method based on the specific situation. Finally, taking the selection of financial products as an example, it shows that the method proposed in this paper has some breakthroughs and advantages.