Significance of the order of pair‐wise comparisons in Analytic Hierarchy Process: an experimental study

Abstract

The article describes an approach, ensuring higher credibility of expert estimation results, based on specific order of pair‐wise comparisons. The order of pair‐wise comparisons is, in its turn, based on the distance between estimated objects in the ranking. According to the suggested approach (and some human psychophysiological features), the most ordinally distant objects should be compared before ordinally closer ones. In order to empirically confirm this assumption, a special experiment involving real experts has been conducted. The results of the experiment indicate that if objects are presented to the expert for comparison in the suggested order, then in the majority of cases relative weights of objects, obtained using eigenvector method, most adequately reflect this expert's priorities. Moreover, pair‐wise comparison matrices constructed using the suggested comparison order tend to be slightly more consistent. The suggested approach to re‐ordering of pair‐wise comparisons can be applied as part of the AHP algorithm in weakly structured subject domains, influenced by multiple intangible criteria. It also provides conceptual basis for reduction of the number of pair‐wise comparisons, required to obtain credible results, in AHP without loss or distortion of expert data. It can also be used for modification of combinatorial pair‐wise comparison aggregation method, based on spanning tree enumeration. And, finally, it will improve the overall multi‐criteria decision‐making process in diverse subject domains, characterized by high uncertainty levels.