成对比较的高效张量基
Efficient tensor bases for pairwise comparisons
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中文总结 AI 辅助
本研究构建了成对比较理论中首个加性一致子空间的正交基，建立了对数一致投影，与Saaty型和SVD型加窗比较得出新复合公式，附有大量示例。
中文摘要 AI 辅助
本研究在成对比较理论中构建了首个加性一致子空间的正交基，该构建基于我们对具有最小支撑的张量基的斜对称矩阵的加性一致最佳逼近的表示。此正交基为成对比较矩阵的正交加窗建立了对数一致投影，我们将其与Saaty型和SVD型加窗进行比较，这些比较得出了对数、Saaty和SVD投影的新复合公式，论文中给出的理论考虑附有大量示例。
英文摘要
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.
