A tool for the Analytic Hierarchy Process based on Leibniz's formula for determinants computation

Abstract

In the Analytic Hierarchy Process (AHP) are expected consistent matrices when the decision-maker performs perfect judgements. Such matrices rarely appear in real situations, since humans do not always decide in the same way. However, understanding these matrices helps to understand the near consistent matrices, which actually occur in real situations. Therefore, in this paper the Leibniz's formula properties are explored for these matrices determinant calculus. The main objective of this approach is to insert, in the AHP framework, new theories to the study of consistent and near consistent matrices. For that, two models of near consistent matrices are implemented, namely multiplicative and additive. In addition, some consequent results are explored, such as, diagonalization and exponential matrix.