A novel group decision-making method for incomplete interval-valued intuitionistic multiplicative linguistic preference relations

By conducting pairwise comparisons, decision-makers can construct interval-valued intuitionistic multiplicative linguistic preference relations (IVIMLPRs) to express the asymmetrically uncertain preferred and non-preferred qualitative judgments. Based on the consistency and consensus analysis, this paper proposes a new group decision-making (GDM) method with incomplete IVIMLPRs. Firstly, a reasonable and rational concept for IVIMLPR is defined. Inspired by the consistent intuitionistic multiplicative linguistic preference relations (IMLPRs), the consistency of IVIMLPRs is expressed by considering the corresponding lower and upper IMLPRs. After that, the acceptably consistent IVIMLPR is further introduced. Based on these concepts, two optimization models are constructed to estimate the missing linguistic variables and adjust an unacceptably consistent IVIMLPR, respectively. To obtain the priority weights from IVIMLPR in a reliable way, the consistency modeling method is employed. Before calculating the collective IVIMLPR, the weights of decision-makers are determined. Subsequently, the consensus analysis is conducted. If the consensus of an IVIMLPR is insufficient, a mathematical model is established to enhance the consensus level. Finally, the applications of the proposed GDM approach are offered and the comparative analysis is discussed. Compared with some existing methods, the proposed decision-making algorithm can perform a rational and effective process in the field of artificial intelligence computing.