Aggregation of two similar opinions expressed by interval pairwise comparison matrices

Abstract

In the Analytic Hierarchy Process (AHP), the criteria importance is given by a Pairwise Comparison Matrix (PCM), whose elements represent the relative importance of items corresponding to the row and column. In collective decision problems, the aggregation of multiple PCMs representing opinions from various viewpoints of members in different positions is important for obtaining outcomes desirable for a big majority. The components of PCMs given by the experts on the problem can be intervals of acceptable values reflecting their wide perspectives. In this paper, we investigate the methods for the aggregation of two opinions expressed by PCMs with interval components given by two experts. We assume that those interval PCMs are similar as both experts give them in consideration of various members in the collective. Moreover, as the given interval PCMs are not always consistent themselves, some method for ensuring consistency, i.e., consistentization should be applied for the given interval PCMs together with the aggregation. Under the problem setting described above, four consistently aggregated methods are formulated and examined. They are different in the application stages of aggregation and consistentization.