Konrad Kułakowski, Ryszard Smarzewski
arXiv 26 Aug 2026 · cs.CE
arXiv:2608.25923 · PDF · Extracted main text
In this study, we construct the first orthogonal basis for additively consistent subspace in pairwise comparisons theory. This construction is based on our representation of additively consistent best approximations of skew-symmetric matrices with respect to a tensor basis having minimal support. The orthogonal basis establishes the logarithmic consistent projection for the orthogonal windowing of pairwise comparisons matrices. It is compared with the windowing of the Saaty and SVD types. These comparisons resulted in new composite formulae for logarithmic, Saaty, and SVD projections. The theoretical considerations presented in the paper are accompanied by numerous examples.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | T. L. Saaty (1980) The analytic hierarchy process: planning, priority setting, resource allocation | 1.000 | 11 | 6 | 100% |
| 2 | W. W. Koczkodaj, R. Smarzewski, and J. Szybowski (2020) On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices | 1.000 | 9 | 5 | 100% |
| 3 | S. I. Gass and T. Rapcsák (2004) Singular value decomposition in AHP | 1.000 | 7 | 5 | 100% |
| 4 | B. Golany and M. Kress (1993) A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices | 1.000 | 7 | 5 | 100% |
| 5 | W. W. Koczkodaj and M. Orlowski (1997) An orthogonal basis for computing a consistent approximation to a pairwise comparisons matrix | 1.000 | 7 | 4 | 100% |
| 6 | R. Smarzewski and P. Rutka (2020) Consistent projections and indicators in pairwise comparisons | 1.000 | 7 | 4 | 100% |
| 7 | T. L. Saaty (1977) A scaling method for priorities in hierarchical structures | 1.000 | 6 | 4 | 100% |
| 8 | S. Bozóki and T. Rapcsák (2008) On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices | 1.000 | 5 | 4 | 100% |
| 9 | T. L. Saaty and L. G. Vargas (1984) Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios | 1.000 | 5 | 4 | 100% |
| 10 | S. Sipahi and M. Timor (2010) The analytic hierarchy process and analytic network process: an overview of applications | 0.928 | 4 | 4 | 100% |
Showing the top 10 of 53 scored citations.