A 0-1 mixed programming model based method for group decision making with intuitionistic fuzzy preference relations

•This paper analyzes the limitations of the previous consistency concepts.•A new concept for intuitionistic fuzzy preference relations (IFPRs) is defined.•0-1 mixed programming models for inconsistent and incomplete IFPRs are built.•A multiplicative consistency and consensus based group decision making is developed.•Numerical examples are offered, and comparison analysis is made.

Intuitionistic fuzzy preference relations (IFPRs) are important and powerful that can express the decision makers' preferred and non-preferred judgements simultaneously. To rank objects reasonably, consistency analysis is necessary. Thus, this paper defines a new multiplicative consistency concept for IFPRs that is a natural extension of the crisp case. Using the new concept, 0-1 mixed programming models are constructed to judge the consistency of IFPRs and to determine missing values in incomplete IFPRs. Considering the inconsistent case, an approach to deriving multiplicative consistent IFPRs is presented. To address group decision making with IFPRs, a consensus index is proposed to measure the agreement degree between individual IFPRs. Then, an approach to group decision making with IFPRs is presented that can address the inconsistent and incomplete IFPRs. Finally, two practical examples are provided to show the efficiency and feasibility of the new theoretical results, and a comparison analysis is performed.