An Alternative Consensus Model of Additive Preference Relations for Group Decision Making Based on the Ordinal Consistency

Pairwise comparison is a useful tool to express decision makers’ (DMs’) preferences in the group decision-making (GDM) problems. However, the preferences provided by pairwise comparisons could be self-contradictory, i.e., ordinal inconsistencies exist. Therefore, before reaching consensus, the first thing is to assure the DM’s judgments that are not contradictory. As the purpose of the GDM is to choose most preferred alternative, the consensus degree for each alternative of all the DMs should be measured. In the present paper, an alternative consensus model for additive preference relations (APRs) based on ordinal consistency (OC) is developed. An algorithm is applied to detect and adjust the ordinally inconsistent elements for APRs. Then the alternative rankings for each ordinally consistent APR and the aggregated APR is obtained, respectively. A model is designed to change the DMs’ importance, which increases the alternative consensus degree. The proposed model does not change the DMs’ preferences, aiming to make full use of the DMs’ judgements. Finally, an illustrative example and comparisons with the current approaches are furnished to demonstrate the effectiveness of the developed method.