Neutrosophic multiplicative preference relations based on consensus analysis and additive consistency in group decision making: A goal programming approach

Multiplicative preference relations can be expanded into Neutrosophic multiplicative preference relations (NMPR) and Interval Neutrosophic Multiplicative Preference Relations (INMPR). They are appropriate for capturing the experts' assessments' uncertainty, ambiguity, and indeterminacy. This work aims to provide a consistency and consensus-based approach for dealing with group decision-making using NMPRs and INMPRs, as well as many goal programming models to manage the consistency and consensus of NMPRs and INMPRs. To define and measure acceptable consistency for NMPRs and INMPRs, the study first offers a consistency index. Several consistency-based programming approaches are designed to address the inconsistency and provide an appropriate consistent NMPR and INMPR for an NMPR and INMPR that are not consistent enough. We provide a consistency-based approach to NMPR and INMPR decision-making. Then, considering the consensus in GDM, a consensus index is suggested for determining the level of agreement between specific NMPRs and INMPRs. Thereafter, a group NMPR and INMPR are created by combining individual NMPRs and INMPRs using an aggregation operator that ensures the consistency of the group NMPRs and INMPRs. With a collection of NMPRs and INMPRs, a consistency- and consensus-based GDM approach is built on single-valued neutrosophic sets (SVNS) and interval-valued neutrosophic sets (IVNS). Finally, two real-world numerical examples are shown, along with a comparison. The proposed method checked the individual consistency level and the group consensus, which is less than the existing method. The ranking of the alternatives was given, which was more convincing than the existing methods. It is also clear that it is much simpler than the previous methods.