Group decision-making based on multiplicative consistency and consensus of linguistic interval-valued q-rung orthopair fuzzy preference relations

In this paper, we delve into a group decision-making (GDM) approach based on incomplete linguistic interval-valued q-rung orthopair fuzzy preference relations (LIVq-ROFPRs), emphasizing the significance of consistency and consensus analysis. The LIVq-ROFPR is defined and the multiplicative consistency is further discussed by introducing the relevant lower and upper linguistic q-rung orthopair fuzzy preference relations (Lq-ROFPRs). Taking into account the consistency level, two programming models are established. One aims at estimating the missing preference information, while the other is designed to rectify an unacceptably multiplicatively consistent LIVq-ROFPR. Utilizing the relationship between the normalized linguistic q-rung orthopair fuzzy priority weight vector and the multiplicatively consistent Lq-ROFPR, we develop a model for deriving the linguistic interval-valued q-rung orthopair fuzzy priority weights. Additionally, we introduce a group consensus index and determine decision-makers’ weights by minimizing this index. To reach an acceptable consensus level, we devise an iterative algorithm and calculate the adjustment parameter in each iteration step, which can theoretically guarantee a steady decrease of the group consensus index during the consensus improving process. Finally, we present two examples to illustrate the practical applications and advantages of our proposed GDM method.