Deriving the priority weights from multiplicative consistent single-valued neutrosophic preference relations

Preference relation is one of the most important and relatively simple approaches to address decision-making problems. As a special case of neutrosophic sets, the single-valued neutrosophic set (SVNS) is an efficient and powerful tool to deal with imprecise and inconsistent information. Taking the advantages of preference relations and SVNSs, this paper introduces single-valued neutrosophic preference relations (SVNPRs). Just as other types of preference relations, consistency and consensus analyses are indispensable to guarantee the ranking order logically. A multiplicative consistency concept for SVNPRs is introduced. On the basis of this concept, several multiplicative consistency-based 0-1 mixed programming models are established to derive multiplicatively consistent SVNPRs and estimate missing values in incomplete SVNPRs, respectively. As for group decision-making, a distance measure-based consensus index is presented. Moreover, an algorithm for group decision-making with SVNPRs is developed, which can deal with incomplete and inconsistent SVNPRs. Finally, a practical example is offered to show the practicability of the new procedure, and comparison is made with several previous methods about decision-making with SVNSs.