| 互补判断矩阵和积排序法的最优化理论基础及性质 |
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| 引用本文： | 周礼刚,陈华友.互补判断矩阵和积排序法的最优化理论基础及性质[J].系统工程与电子技术,2004,26(9):1209-1211. |
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| 作者姓名： | 周礼刚 陈华友 |
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| 作者单位： | 1. 安徽大学数学系,安徽,合肥,230039
2. 安徽大学数学系,安徽,合肥,230039;南京大学工程管理学院,江苏,南京,210093 |
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| 基金项目： | 安徽省教育厅科研基金(2002kj022)，中国博士后科学基金资助课题(20040350189) |
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| 摘 要： | 针对多属性决策中重要的方法之一的互补判断矩阵和积排序法,在完全一致性互补判断矩阵等概念的基础上,给出了互补判断矩阵和积排序法的最优化理论基础,指出互补判断矩阵和积排序法的排序向量正好是某种偏差准则下的最优化模型的解。并证明了它具有一些性质,包括强条件下保序性,置换不变性等。最后举出反例说明它不具备对称性。
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| 关 键 词： | 多属性决策 互补判断矩阵 和积排序法 最优化模型 |
| 文章编号： | 1001-506X(2004)09-1209-03 |
| 修稿时间： | 2003年7月27日 |
Optimization basis and properties of the sum-product method of complementary judgement matrix |
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| ZHOU Li-gang,CHEN Hua-you.Optimization basis and properties of the sum-product method of complementary judgement matrix[J].System Engineering and Electronics,2004,26(9):1209-1211. |
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| Authors: | ZHOU Li-gang CHEN Hua-you |
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| Institution: | ZHOU Li-gang~1,CHEN Hua-you~ |
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| Abstract: | The sum-product method of complementary judgement matrix is one of the important priority methods in multiple attribute decision-making. Based on the concept of consistency of complementary judgement matrix and other concepts, the optimization basis of the sum-product priority method is given. It is pointed out that sum-product priority vectors are the solutions of optimal model under certain deviation criteria. Some properties, such as rank preservation, permutation invariability, compatibility, are also proved. Finally a counter example shows that this method doesn't have symmetry. |
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| Keywords: | multiple attribute decision-making complementary judgement matrix sum-product priority method optimal model |
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