On the coincidence of optimal completions for small pairwise comparison matrices with missing entries

László Csató, Kolos Agoston and Sándor Bozóki ()
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Sándor Bozóki: HUN-REN Institute for Computer Science and Control (HUN-REN SZTAKI)

Annals of Operations Research, 2024, vol. 333, issue 1, No 8, 239-247

Abstract: Abstract Incomplete pairwise comparison matrices contain some missing judgements. A natural approach to estimate these values is provided by minimising a reasonable measure of inconsistency after unknown entries are replaced by variables. Two widely used inconsistency indices for this purpose are Saaty’s inconsistency index and the geometric inconsistency index, which are closely related to the eigenvector and the logarithmic least squares priority deriving methods, respectively. The two measures are proven to imply the same optimal filling for incomplete pairwise comparison matrices up to order four but not necessarily for order at least five.

Keywords: Analytic Hierarchy Process (AHP); Decision analysis; Eigenvalue method; Incomplete pairwise comparisons; Logarithmic least squares method; 90-10; 90B50; 91B08 (search for similar items in EconPapers)
JEL-codes: C44 D71 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05586-x

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