Chi-square method for Checking Consistency in Analytic Hierarchy Process (AHP)

Wan Rosanisah Wan Mohd, Lazim Abdullah

One of the outstanding methods of multi-criteria decision-making (MCDM) is the Analytic Hierarchy Process (AHP). Basically, the AHP is constructing a decision matrix by comparing two or more objects. This is known as the pairwise comparison matrix (PCM). The PCM is vital in decision making as it is a matrix decision that represents the decision makers’ (DMs) preferences. The common issues of the PCM are the consistency of the decision matrix. Checking consistency is prerequisite to ensure the judgments/preferences of the DMs are made is logical. Neglecting the consistency check will tend to the incorrect final decisions. The first method of consistency check is the eigenvalue method (EVM) proposed by Saaty in AHP. However, the effectiveness of these consistency checks is not immediately known. In the other way, the consistency of PCM of AHP can be investigated with chi-square consistency index method. The main goal of this study is to determine the consistency index and consistency ratio of AHP using chi-square consistency index method. Some numerical examples are presented to demonstrate the chi-square consistency index method. Finally, the result shows that the chi-square method is more relevant and acceptable in representing the actual data.

Volume 11 | 12-Special Issue

Pages: 214-220