A mathematical programming approach to manage group decision making with incomplete hesitant fuzzy linguistic preference relations

Abstract

Hesitant fuzzy linguistic information can be a useful decision-making tool in uncertain and complex environments. In this paper, we establish a new group decision making (GDM) model based on mathematical programming with incomplete hesitant fuzzy linguistic preference relations (HFLPRs). After developing a definition of incomplete HFLPR and its multiplicative consistency, we propose an equivalence theorem of multiplicative consistency between linguistic preference relation (LPR) and corresponding fuzzy preference relation (FPR). Based on this framework, a mathematical programming to address incomplete HFLPR is established. The proposed mathematical programming method has the dual functionality of finding the incomplete LPR with the highest consistency and increasing inconsistent LPR to complete consistent LPR using multiplicative consistency based on given incomplete HFLPR. In this manner, we construct a novel GDM model based on obtained multiplicative consistency LPRs in consideration of the group consensus reaching process. Finally, a real-world emergency management problem is solved to demonstrate the effectiveness of the proposed GDM model.