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

Csató, László ORCID: https://orcid.org/0000-0001-8705-5036, Ágoston, Kolos Csaba and Bozóki, Sándor ORCID: https://orcid.org/0000-0003-4170-4613 (2024) On the coincidence of optimal completions for small pairwise comparison matrices with missing entries. Annals of Operations Research, 333 (1). pp. 239-247. DOI 10.1007/s10479-023-05586-x

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Official URL: https://doi.org/10.1007/s10479-023-05586-x

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.

Item Type:

Article

Uncontrolled Keywords:

Decision analysis; analytic hierarchy process (AHP); D71; eigenvalue method; Incomplete pairwise comparisons; Logarithmic least squares method; C44; 90-10;

JEL classification:

C44 - Operations Research; Statistical Decision Theory
D71 - Analysis of Collective Decision-Making: Social Choice; Clubs; Committees; Associations

Divisions:

Institute of Operations and Decision Sciences

Subjects:

Decision making

DOI:

10.1007/s10479-023-05586-x

ID Code:

10014

Deposited By:

MTMT SWORD