Heterogeneous group decision making in the setting of incomplete preference relations

This paper focuses on heterogeneous group decision making (GDM) in the setting of incomplete preference relations, including incomplete fuzzy preference relations, incomplete multiplicative preference relations, incomplete additive linguistic preference relations, and incomplete multiplicative linguistic preference relations. Following the consistency-consensus optimization analysis, a new GDM method is proposed which can address inconsistent and incomplete preference relations. Firstly, we consider how to determine unknown information and how to obtain consistent preference relations. In contrast to the existing methods which rank the alternatives from fuzzy preference relations using the additive or multiplicative consistency analysis, this paper follows the consistency level to decide to use the additive or multiplicative consistency. Following the consensus analysis for each type of consistent preference relations, we calculate their comprehensively consistent preference relations and the priority vectors. After that, we build a consistency-based model for calculating the comprehensive priority vector. Furthermore, we offer an ordered position consensus-based method using the built optimization models. The proposed heterogeneous GDM method with incomplete preference relations provides us with a very useful way for dealing with GDM problems in heterogeneous environments.