Exploiting the priority weights from interval linguistic fuzzy preference relations

Interval linguistic fuzzy preference relations (ILFPRs) are powerful tools to denote the decision makers' uncertain qualitative preferences. To avoid the inconsistent ranking results, consistency analysis is very critical. This paper introduces a new additive consistency concept for ILFPRs, which satisfies all properties of the additive consistency concept for fuzzy preference relations. Then, a model to judging the additive consistency of ILFPRs is constructed. When ILFPRs are inconsistent, an approach to deriving additive consistent ILFPRs is presented. Considering the incomplete case, goal programming models to determining the missing values are established. Subsequently, a distance measure-based group consensus index is given to measuring the consensus of individual ILFPRs. Furthermore, a new method for group decision making with ILFPRs is developed, which is based on the additive consistency and consensus analysis. Finally, two numerical examples are offered to show the application of the developed procedure, and a comparison analysis is performed.