On the coincidence of optimal completions for small pairwise comparison matrices with missing entries
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917583164276736 |
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| author | Csató, László Ágoston, Kolos Csaba Bozóki, Sándor |
| author_facet | Csató, László Ágoston, Kolos Csaba Bozóki, Sándor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07976 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the coincidence of optimal completions for small pairwise comparison matrices with missing entries Csató, László Ágoston, Kolos Csaba Bozóki, Sándor Optimization and Control 90-10, 90B50, 91B08 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. |
| title | On the coincidence of optimal completions for small pairwise comparison matrices with missing entries |
| topic | Optimization and Control 90-10, 90B50, 91B08 |
| url | https://arxiv.org/abs/2211.07976 |