Consistent projections and indicators in pairwise comparisons
Consistent projections and indicators in pairwise comparisons
复制标题
DOI：
10.1016/j.ijar.2020.06.001
复制
发表时间：
2020-09-01
影响因子：
3.9
通讯作者：
Rutka, Przemyslaw
中科院分区：
文献类型：
--
作者：
Smarzewski, Ryszard;Rutka, Przemyslaw
本研究检查了方阵的任意有限维内积空间中加权一致投影的几个通用属性和不一致性指标。对于加权弗罗贝尼乌斯内积，我们根据矩阵项和权重给出了明确的公式。它扩展了 Koczkodaj 等人最近的结果。 [基金。通知。 172 (2020) 379-397]，成对比较中的正矩阵。此外，我们讨论了基于正交一致投影的数值应用正确选择内积权重的可能性。 (C) 2020 Elsevier Inc. 保留所有权利。
This study examines several generic properties of weighted consistent projections and indicators of inconsistency in an arbitrary finite dimensional inner product space of square matrices. In the case of weighted Frobenius inner products we present explicit formulae for them in terms of the matrix entries and weights. It extends the recent results, due to Koczkodaj et al. [Fund. Inform. 172 (2020) 379-397], to positive matrices in pairwise comparisons. Moreover, we discuss the possibilities of a proper choice of the inner product weights for numerical applications based on the orthogonal consistent projections. (C) 2020 Elsevier Inc. All rights reserved.