论文标题
在一致的成对比较矩阵上的正交投影上
On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices
论文作者
论文摘要
在这项研究中，将不同内部产物的正交过程应用于成对比较。检查给定不一致的成对比较矩阵的一致近似值的属性。已经引入了通过成对比较矩阵诱导的优先矢量的推导方法。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这项研究的激励因素。但是，这项研究的发现近似取决于所假定的内部产品，至关重要。
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.
