Goal Programming Approaches to Managing Consistency and Consensus for Intuitionistic Multiplicative Preference Relations in Group Decision Making

Intuitionistic multiplicative preference relations (IMPRs), as an extension of multiplicative preference relations (MPRs), are suitable to capture hesitation and indeterminacy of the experts' judgments. This paper aims to build several goal programming models to manage consistency and consensus of IMPRs and develop a consistency and consensus-based approach for dealing with group decision making (GDM) with IMPRs. First, the study offers a consistency index to quantify the consistency level for IMPRs as well as to define acceptably consistent IMPRs. For an IMPR, which is unacceptably consistent, several consistency-based programming models are developed to deal with the inconsistency and to establish an acceptable consistent IMPR. A consistency-based method to decision making with an IMPR is presented. Subsequently, considering the consensus in GDM, a consensus index is proposed for gauging the agreement degree among individual IMPRs. As to the individual IMPRs, which do not exhibit acceptable consistency or acceptable consensus, several goal programming models to derive new IMPRs with acceptable consistency and consensus are provided. Afterward, individual IMPRs are fused into a group IMPR by an aggregation operator that can guarantee the consistency of the obtained group IMPR. A consistency and consensus-based GDM method with a group of IMPRs is developed. Finally, two practical numerical examples are offered and a comparative analysis is presented.