Barzilai 基本定理不成立
最优化与控制
2021-02-11 v3
摘要
Barzilai, J. (1997) 发表于 Journal of the Operational Research Society, 48(12), 1226-1232 的被广泛引用的著作《从成对比较矩阵导出权重》，从两个简单公理推导出了几何平均法。本注记揭示，该文被称为作者基本定理的核心结果并不成立，因为至少存在另一种满足两项要求的方法。
引用
@article{arxiv.1912.05968,
title = {The Fundamental Theorem of Barzilai does not hold},
author = {Dóra Gréta Petróczy and László Csató},
journal= {arXiv preprint arXiv:1912.05968},
year = {2021}
}
备注
Proposition 1 does not hold as the column mean method does not meet independence of relative measurements due to the normalisation of the weights