  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.
