Inferring consensus weights from pairwise comparison matrices without suitable properties

Abstract

Pairwise comparison is a popular method for establishing the relative importance of n objects. Its main purpose is to get a set of weights (priority vector) associated with the objects. When the information gathered from the decision maker does not verify some rational properties, it is not easy to search the priority vector. Goal programming is a flexible tool for addressing this type of problem. In this paper, we focus on a group decision-making scenario. Thus, we analyze different methodologies for getting a collective priority vector. The first method is to aggregate general pairwise comparison matrices (i.e., matrices without suitable properties) and then get the priority vector from the consensus matrix. The second method proposes to get the collective priority vector by formulating an optimization problem without determining the consensus pairwise comparison matrix beforehand.