Additive Consistency Analysis for Picture Fuzzy Preference Relation

As a generalization of intuitionistic fuzzy set, picture fuzzy set is characterized by positive membership, neutral membership and negative membership. The picture fuzzy preference relation (PFPR), whose elements are picture fuzzy numbers, is stronger than intuitionistic fuzzy preference relation in expressing comprehensive preference information of decision-makers. This paper will focus on the additive consistency of PFPR. Firstly, a novel score function is proposed to obtain stable and consistent score values for ranking the alternatives. Then, the additive consistency of PFPR and normalized picture fuzzy priority weight vectors are studied. Subsequently, six goal programming models are proposed to generate the priorities from individual and group PFPRs, respectively. Finally, three numerical examples are provided to illustrate the flexibility and rationality. What's more, the effectiveness is verified by comparing it with some existing methods.