🤖 AI Summary
本文通过构建具有最小支撑的张量基，解决了成对比较理论中加性一致子空间的正交基问题，并提出了新的对数、Saaty和SVD投影公式。
📝 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.