Approaches to group decision making with intuitionistic fuzzy preference relations based on multiplicative consistency

The intuitionistic fuzzy preference relation (IFPR) was introduced by Xu to efficiently deal with situations in which the decision makers (DMs) exhibit the characteristics of affirmation, negation and hesitation for the preference degrees over paired comparisons of alternatives. In this paper, two new approaches to group decision making (GDM) are proposed to derive the normalized intuitionistic fuzzy priority weights from IFPRs based on the order consistency and the multiplicative consistency. First, the concepts of order consistency and weak transitivity for IFPRs are introduced, and followed by a discussion of their desirable properties. Then, in order to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFPR, a transformation approach is investigated. Two linear optimization models are further developed to derive the normalized intuitionistic fuzzy weight vector for both individual and group IFPRs with the principle of minimizing the deviations between any provided IFPR and the converted multiplicative consistent IFPR, and the optimal deviation values obtained from the models enable us to improve the multiplicative consistency of IFPRs. Finally, based on the order consistency and the multiplicative consistency, two new algorithms for GDM are presented. Several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate that the proposed methods are both valid and practical to deal with group decision making problems.