Group decision making based on multiplicative consistent reciprocal preference relations

The main aim of this paper is to investigate the consistency and consensus of multiplicative consistent reciprocal preference relations. Based on the multiplicative consistency property, a straightforward method to obtain the priority vector for multiplicative consistent reciprocal preference relation is introduced together with some of its desired properties. In addition, some interesting properties on consistency and consensus for reciprocal preference relations are further investigated. A consensus optimization model for group decision making with reciprocal preference relations is proposed, which enables the decision makers to reach consensus with the highest overall consensus level. Numerical examples are provided to make a discussion and comparison with some existing similar methods.