An improvement of multiplicative consistency of reciprocal preference relations: A framework of granular computing

The commonly used preference elicitation method in decision making is the one using pairwise comparison between alternatives. In this kind of decision making scenario, an essential issue requiring attention is that of consistency, particularly in decision problems with numerous alternatives. Consistency is usually linked to the transitivity concept, which is modeled in several diverse ways. Given the importance of avoiding conflicting opinions in decision making, in this study, we propose an approach to improve the consistency when reciprocal preference relations are used. On one hand, consistency is modeled in terms of the multiplicative transitivity property. On the other hand, information granularity is used to introduce and develop the concept of interval reciprocal preference relations in which the entries are constructed as intervals in place of single numeric values. This provides the necessary flexibility to improve the consistency. To illustrate and test the performance of the approach that is proposed here, an example is given.