Simulation Research on the Relationship between Selected Inconsistency Indices Used in AHP

The Analytic Hierarchy Process (AHP) is a widely used used multi-criteria decision-making method (MCDM). This method is based on pairwise comparison, which forms the so-called Pairwise Comparison Matrix (PCM). PCMs usually contain some errors, which can have an influence on the eventual results. In order to avoid incorrect values of priorities, the inconsistency index (ICI) has been introduced in the AHP by Saaty. However, the user of the AHP can encounter many definitions of ICIs, of which values are usually different. Nevertheless, a lot of these indices are based on a similar idea. The values of some pairs of these indices are characterized by high values of a correlation coefficient. In my work, I present some results of Monte Carlo simulation, which allow us to observe the dependencies in AHP. I select some pairs of ICIs and I evaluate values of the Pearson correlation coefficient for them. The results are compared with some scatter plots that show the type of dependencies between selected ICIs. The presented research shows some pairs of indices are closely correlated so that they can be used interchangeably.