Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Kułakowski, Konrad, Smarzewski, Ryszard
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Funder: Narodowym Centrum Nauki
OpenAlex ID: W7204493827
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