A Simplified Algorithm for Dealing with Inconsistencies Using the Analytic Hierarchy Process

Abstract

Inconsistencies in the comparison matrix is a common problem in many studies using the analytic hierarchy process (AHP). While these may be identified and corrected through asking respondents to reconsider their choices, this is not always possible. This is particularly the case for online surveys, where the number of respondents may be large and often anonymous, such that interacting with individual respondents is neither feasible nor possible. Several approaches have previously been developed for autonomously adjusting the comparison matrix to deal with inconsistencies. In this paper, we build on these previous approaches, and present an algorithm that is conceptually and analytically simple and readily implementable in R. The algorithm is applied to several example cases to illustrate its performance, including an example case study involving data collected through a large online survey. The results suggest that the modified survey-derived comparison matrix derived using the algorithm produces consistent responses that do not substantially alter the individual preferences in most cases.