Incomplete pairwise comparison matrices and their applications
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911548373467136 |
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| author | Csató, László Bozóki, Sándor |
| author_facet | Csató, László Bozóki, Sándor |
| contents | Incomplete pairwise comparison matrices are increasingly employed to save resources and reduce cognitive load by collecting only a subset of all possible pairwise comparisons. We present their graph representation and some completion algorithms, including the incomplete eigenvector and incomplete logarithmic least squares methods, as well as a lexicographical minimisation of triad inconsistencies. The issue of ordinal violations is discussed for matrices generated by directed acyclic graphs and the best--worst method. We also show a reasonable approach to generalise the inconsistency threshold based on the dominant eigenvalue to the incomplete case, and state recent results on the optimal order of obtaining pairwise comparisons. The benefits of using incomplete pairwise comparisons are highlighted by several applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26552 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Incomplete pairwise comparison matrices and their applications Csató, László Bozóki, Sándor Optimization and Control 90B50, 91B06 Incomplete pairwise comparison matrices are increasingly employed to save resources and reduce cognitive load by collecting only a subset of all possible pairwise comparisons. We present their graph representation and some completion algorithms, including the incomplete eigenvector and incomplete logarithmic least squares methods, as well as a lexicographical minimisation of triad inconsistencies. The issue of ordinal violations is discussed for matrices generated by directed acyclic graphs and the best--worst method. We also show a reasonable approach to generalise the inconsistency threshold based on the dominant eigenvalue to the incomplete case, and state recent results on the optimal order of obtaining pairwise comparisons. The benefits of using incomplete pairwise comparisons are highlighted by several applications. |
| title | Incomplete pairwise comparison matrices and their applications |
| topic | Optimization and Control 90B50, 91B06 |
| url | https://arxiv.org/abs/2603.26552 |