In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation of a priority vector induced by a pairwise comparison matrix for a given inner product has been introduced. The mathematical elegance of orthogonalization and its universal use in most applied sciences has been the motivating factor for this study. However, the finding of this study that approximations depend on the inner product assumed, is of considerable importance.

中文翻译：

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关于一致成对比较矩阵空间的正交投影

在这项研究中，不同内积的正交化过程应用于成对比较。检查给定的不一致成对比较矩阵的一致近似的性质。已经介绍了由给定内积的成对比较矩阵导出的优先向量的推导方法。正交化的数学优雅及其在大多数应用科学中的普遍使用一直是本研究的推动因素。然而，本研究发现近似值取决于假设的内积，这一发现非常重要。