Multi-criteria group decision-making based on quasi-order for dual hesitant fuzzy sets and professional degrees of decision makers

Dual hesitant fuzzy set (DHFS) is a useful tool that can assist the decision makers (DMs) to express their evaluation information more flexibly from two contrary points of view, which are the membership degrees and the non-membership degrees. In this paper, we mainly focus on the quasi-order for DHFSs and the professional degrees of the DMs in multi-criteria group decision-making (MCGDM) under dual hesitant fuzzy information. First, we define a quasi-order for DHFSs based on pairwise comparisons. The quasi-order could distinguish two different DHFSs more clearly and rationally. Second, we propose the professional degrees of the DMs based on dual hesitant fuzzy information and use the professional degrees to determine the weights of the DMs. The professional degrees could indicate the weights of the DMs from different viewpoints in MCGDM more reliably. In the process of decision-making, the professional degree of each DM to the decision-making problem could influence the final decision directly. On the one hand, the evaluation information has a close-knit relationship with the professional degree of each DM. On the other hand, the professional degrees of the DMs should be a very important aspect to determine the weights of the DMs directly. In addition, we combine the quasi-order and the professional degrees in MCGDM. Finally, we use a practical numerical example on the rural land conversion to illustrate the availability and practicability of the proposed MCGDM model.