Construction and restrictions of consistent matrices by Macharis’ method

Abstract

In 2004, Macharis et al. proposed a consistent comparison matrix. In this study, we provide a patch work for discussing the construction and restrictions of their consistent comparison matrix. Their study is important in academia and has been cited by over 200 papers. However, in the article, the authors neither provide a detailed explanation on how to construct the proposed revised consistent comparison matrix nor mention any restriction when constructing it. In this study, we not only propose an algorithm to construct the consistent matrix, but also prove that two restrictions exist when developing a sequence of their consistent comparison matrices, which are: (a) the changing of entries should follow a decreasing order with respect to the row index and (b) there is at most one entry in each row that can be revised by experts. The results of this study will help researchers properly apply the consistent matrices proposed by Macharis et al. (2004) in the future.