[1]徐泽水,达庆利.两种修正判断矩阵一致性方法的比较分析[J].东南大学学报(自然科学版),2002,32(6):913-916.[doi:10.3969/j.issn.1001-0505.2002.06.019]
 Xu Zeshui,Da Qingli.Analysis and comparison of two methods for improving consistency of judgement matrix[J].Journal of Southeast University (Natural Science Edition),2002,32(6):913-916.[doi:10.3969/j.issn.1001-0505.2002.06.019]
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两种修正判断矩阵一致性方法的比较分析()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
32
期数:
2002年第6期
页码:
913-916
栏目:
数学、物理学、力学
出版日期:
2002-11-20

文章信息/Info

Title:
Analysis and comparison of two methods for improving consistency of judgement matrix
作者:
徐泽水 达庆利
东南大学经济管理学院, 南京 210096
Author(s):
Xu Zeshui Da Qingli
College of Economics and Management, Southeast University, Nanjing, 210096 China
关键词:
判断矩阵 一致性 收敛
Keywords:
judgement matrix consistency convergence
分类号:
O223
DOI:
10.3969/j.issn.1001-0505.2002.06.019
摘要:
对层次分析法中判断矩阵一致性的修正方法进行了研究, 证明了修正判断矩阵一致性的加权算术平均法的收敛性, 并同加权几何平均法进行了详细的比较. 理论分析表明: 虽然这2种方法都具有收敛性, 且均可对一致性较差的判断矩阵进行修正,但加权几何平均法比加权算术平均法简洁, 且前者无需通过转换, 直接保持了修正后的判断矩阵的互反性. 数值结果也显示:加权几何平均法所需的迭代次数比加权算术平均法所需迭代次数少.
Abstract:
The methods for improving consistency of judgement matrix in the analytic hierarchy process are studied. The convergence of the weighted arithmetic mean method for improving consistency of judgement matrix is proven, and the comparison between the weighted arithmetic mean method and the weighted geometric mean method is also given in detail. Theoretical analysis shows that both methods are of convergence and can be used to improve the judgement matrix with unacceptable consistency. However, the weighted geometric mean method is simpler than the weighted arithmetic mean method, and the former can keep the reciprocity of the improved judgement matrix without transformation. The numerical results also indicate that the weighted geometric mean method needs less number of iteration than the weighted arithmetic mean method.

参考文献/References:

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[7] 陈宝谦,李淑冰,刘桂茹,等.正互反阵的一个特阵值问题[J].高校应用数学学报,1991,6(1):57-65.
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备注/Memo

备注/Memo:
基金项目: 国家自然科学基金资助项目(79970093)、东南大学-南瑞继保公司学位论文基金资助项目.
作者简介: 徐泽水(1968—), 男, 博士生, 副教授; 达庆利(联系人), 男, 教授, 博士生导师, dql@public1.ppt.js.cn.
更新日期/Last Update: 2002-11-20