A consistency and consensus-based method to group decision making with interval linguistic preference relations

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.