Towards quantification of incompleteness in the pairwise comparisons method
arXiv:1812.03589 · doi:10.1016/j.ijar.2019.10.002
Abstract
Alongside consistency, completeness of information is one of the key factors influencing data quality. The objective of this paper is to define ways of treating missing entries in pairwise comparisons (PC) method with respect to inconsistency and sensitivity. Two important factors related to the incompleteness of PC matrices have been identified, namely the number of missing pairwise comparisons and their arrangements. Accordingly, four incompleteness indices have been developed, simple to calculate, each of them take into account both: the total number of missing data and their distribution in the PC matrix. A numerical study of the properties of these indices has been also conducted using a series of Montecarlo experiments. It demonstrated that both incompleteness and inconsistency of data equally contribute to the sensitivity of the PC matrix. Although incompleteness is only just one of the factors influencing sensitivity, a relative simplicity of the proposed indices may help decision makers to quickly estimate the impact of missing comparisons on the quality of final result.
12 pages, 7 figures
References in corpus (5)
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- Inconsistency in the ordinal pairwise comparisons method with and without ties
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Cited by in corpus (7)
- Inconsistency indices for incomplete pairwise comparisons matrices
- Filling in pattern designs for incomplete pairwise comparison matrices: (quasi-)regular graphs with minimal diameter
- Towards secure judgments aggregation in AHP
- On the similarity between ranking vectors in the pairwise comparison method
- Optimal sequences for pairwise comparisons: the graph of graphs approach
- Almost optimal manipulation of a pair of alternatives
- Detection of decision-making manipulation in the pairwise comparisons method