A Consistency and Consensus-Based Goal Programming Method for Group Decision-Making With Interval-Valued Intuitionistic Multiplicative Preference Relations

Interval-valued intuitionistic multiplicative preference relations (IVIMPRs) form a suitable conceptual framework to represent and process simultaneously uncertain preferred and nonpreferred judgments of decision makers (DMs). The focus of this paper is on group decision-making (GDM) problems realized with IVIMPRs. First, a consistency index is introduced to evaluate the consistency degree for intuitionistic multiplicative preference relations (IMPRs), and a consistency optimization approach is presented to jointly improve the consistency degrees of several IMPRs that do not satisfy the predefined consistency threshold. Then, a consistency definition and an acceptable consistency definition for IVIMPRs are established by splitting an IVIMPR into two IMPRs. For several IVIMPRs with unacceptable consistency, a goal program-based approach is proposed to simultaneously improve their consistency. Subsequently, by minimizing the degree to which the opinions of individual DMs deviate from those of the group, a maximum consensus-based goal program is established to determine the DMs' weights. Furthermore, an aggregation approach is applied to integrate individual IVIMPRs into a collective one. A linear program is then built to determine the interval-valued intuitionistic multiplicative priority weights of alternatives coming from the collective IVIMPR. A consistency-based GDM algorithm is proposed. Finally, a practical example is offered to show the application of the new algorithm, and a comparative analysis is presented to highlight the advantages of the new method.