A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy preference relations

To express the uncertain preferred and non-preferred qualitative judgments of decision makers, interval-valued intuitionistic linguistic fuzzy sets (IVILFSs) are proposed in a similar way as Atanassov and Gargov’s interval-valued intuitionistic fuzzy sets. Considering the application of IVILFSs, the concept of interval-valued intuitionistic linguistic fuzzy variables (IVILFVs) is defined and a ranking order is offered. Then, we introduce interval-valued intuitionistic linguistic fuzzy preference relations (IVILFPRs) whose elements are IVILFVs. Furthermore, an additive consistency concept is presented and a model for judging the consistency of IVILFPRs is built. Meanwhile, optimization models for deriving additively consistent IVILFPRs and for determining missing linguistic variables in incomplete IVILFPRs are constructed, respectively. For group decision making, optimization models for determining the weights of the decision makers and for improving the consensus level are established, respectively. A procedure for group decision making with IVILFPRs is developed that can cope with inconsistent and incomplete IVILFPRs. Finally, a practical group decision-making problem about evaluating express companies is selected to show the application of the new results.