Group decision making with multiplicative interval linguistic hesitant fuzzy preference relations

This paper proposes multiplicative interval linguistic hesitant fuzzy sets (MILHFSs) to denote the asymmetrically qualitative judgments with uncertain and hesitant characteristics, which are expressed by several interval linguistic judgments defined on the asymmetrical linguistic term set. Considering the utilization of MILHFSs, the concept of multiplicative interval linguistic hesitant fuzzy variables (MILHFVs) is introduced, and multiplicative interval linguistic hesitant fuzzy preference relations (MILHFPRs) are proposed. Then, we analyze the consistency and introduce an approach for computing the priority vector from consistent MILHFPRs. Meanwhile, incomplete MILHFPRs are discussed, and a model for obtaining unknown MILHFVs following the analysis of consistency is built. Considering group decision making (GDM), the analysis of consensus is made. Subsequently, an approach for GDM with inconsistent and incomplete MILHFPRs is provided that follows the analysis of consistency and consensus. The feasibility of the developed results is demonstrated by two practical GDM problems: (1) assessing seven-seat sport utility vehicles (SUVs) and (2) selecting the public-private partnership (PPP) model. (C) 2019 Elsevier Inc. All rights reserved.