Group decision making with q-rung orthopair hesitant fuzzy preference relations

Abstract: This paper mainly studies group decision making (GDM) problem based on q-rung orthopair hesitant fuzzy preference relations (q-ROHFPRs). First, the definitions of q-ROHFPR and additive consistent q-ROHFPR are introduced. The consistency index of q-ROHFPR is used to judge whether the matrix of q-ROHFPR is acceptable. For the q-ROHFPR matrix that does not meet the acceptable consistency, two optimization models are established for deriving the acceptably additive consistent q-ROHFPRs. In order to make the q-ROHFPR matrix of decision makers still satisfy the consistency after aggregation, this paper extends the q-rung orthopair hesitant fuzzy weighted geometric average operator (q-ROHFWGA). At the same time, in order to verify whether decision makers can reach consensus after aggregation, a consensus index based on distance is offered. Based on this consensus index, an optimization model that satisfies consistency and consensus is constructed to solve the priority vector, and develop a consistency and consensus-based approach for dealing with group decision-making (GDM) with q-ROHFPRs. Finally, the case in this paper verifies the validity and accuracy of the group decision-making model, and also verifies that the q-ROHFPR consistency and consensus management model proposed in this paper can solve the q-rung orthopair hesitant fuzzy preference group decision-making problem.