Dynamic thresholds of geometric consistency index associated with pairwise comparison matrix

Abstract

Pairwise comparison matrix (PCM) has been widely employed in the multi-criteria decision-making (MCDM) problems to rank the criteria and alternatives according to the considered criteria in Analytic Hierarchy Process (AHP). The PCM should have the acceptable consistency before deriving a priority vector from it. Approximate thresholds of geometric consistency index (GCI) and consistency ratio (CR) have been proposed to test whether the PCM has the acceptable consistency. However, approximate thresholds of GCI and CR always suffer from some criticisms and disagreements in existing literature. In this paper, we try to induce dynamic thresholds of GCI by combining hypothesis testing and random index (RI), which vary with the order of the PCM, significance level and assessment level of decision maker. The induced dynamic thresholds of GCI may explain different (or conflicting) results obtained by approximate thresholds of GCI and CR and avoid the unnecessary revisions of some judgments of the PCM for the desired consistency. Finally, several numerical examples and real-world decision-making problems are examined and compared with existing decision-making methods to illustrate the performance of dynamic thresholds of GCI.

Keywords

• analytic hierarchy process
• pairwise comparison matrix
• geometric consistency index
• dynamic thresholds