Inconsistency indices for incomplete pairwise comparisons matrices

Abstract

Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for determining the level of inconsistency among compared alternatives. Unfortunately, most of them assume that the set of comparisons is complete, i.e. every single alternative is compared to each other. This is not true and the ranking must sometimes be made based on incomplete data. In order to fill this gap, this work aims to adapt the selected twelve existing inconsistency indices for the purpose of analyzing incomplete data sets. The modified indices are subjected to Monte Carlo experiments. Those of them that achieved the best results in the experiments carried out are recommended for use in practice.

arXiv comment30 pages, 5 figures

References in corpus (9)

• Axiomatic properties of inconsistency indices for pairwise comparisons
• On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
• The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices
• New results on inconsistency indices and their relationship with the quality of priority vector estimation
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Cited by in corpus (10)

• On the geometric mean method for incomplete pairwise comparisons
• The incomplete Analytic Hierarchy Process and Bradley-Terry model: (in)consistency and information retrieval
• Towards secure judgments aggregation in AHP
• On the similarity between ranking vectors in the pairwise comparison method
• The logarithmic least squares priorities and ordinal violations in the best-worst method
• Inconsistency thresholds for incomplete pairwise comparison matrices
• Almost optimal manipulation of a pair of alternatives
• Optimal sequences for pairwise comparisons: the graph of graphs approach
• Detection of decision-making manipulation in the pairwise comparisons method
• Manipulation of individual judgments in the quantitative pairwise comparisons method