Towards quantification of incompleteness in the pairwise comparisons methods

Abstract

Apart from consistency, the completeness of information is one of the key factors influencing data quality. In the case of the pairwise comparisons (PC) method, much space in the literature is devoted to the quantitative analysis of this first idea, while the second issue has not been properly studied. The presented article is an attempt to bridge this gap. The aim of the article is to examine how the incompleteness of a set of paired comparisons influences the sensitivity of the PC method.During the research, two important factors related to the incompleteness of PC matrices have been identified, namely the number of missing pairwise comparisons and their arrangements. Accordingly, an easy-to-calculate incompleteness index have been developed. It takes into account both the total number of missing data and their distribution in the PC matrix. During the series of Montecarlo experiments, the properties of this index have been examined. It demonstrated that both the incompleteness and inconsistency of data almost equally contribute to the sensitivity of the PC matrix. The relative simplicity of the proposed index may help decision makers to quickly estimate the impact of missing comparisons on the quality of final results.