| 衡量判断矩阵相容性的一个通用指标 |
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| 引用本文： | 徐泽水,达庆利.衡量判断矩阵相容性的一个通用指标[J].东南大学学报(自然科学版),2001,31(6):94-97. |
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| 作者姓名： | 徐泽水 达庆利 |
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| 作者单位： | 1. 东南大学经济管理学院,南京,210096;解放军理工大学理学院,南京,210016
2. 东南大学经济管理学院,南京,210096 |
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| 基金项目： | 国家自然科学基金资助项目 ( 79970 0 93) |
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| 摘 要： | 首先介绍了互反判断矩阵与互补判断矩阵之间的转换公式，以及完全一致性互反判断矩阵和完全一致性互补判断矩阵之间的关系。然后在综合考虑互反判断矩阵与互判断矩阵各自特点的基础上，给出了衡量判断矩阵（包括互反判断矩阵和互补判断矩阵）相容性的一个通用指标，以及互反权重矩阵和互补权重矩阵等概念。对判断矩阵的相容性和一致性详细地进行了研究，并给出了衡量判断矩阵相容性准则。这些结果在群组决策中具有良好的应用前景，有助于进一步提高决策的合理性和有效性，最后进行了算例分析。
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| 关 键 词： | 判断矩阵 相容性 一致性 权重矩阵 群体决策 衡量指标 |
| 文章编号： | 1001-0505(2001)06-0094-04 |
A Common Compatibility Index of Judgement Matrices |
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| Xu Zeshui , Da Qingli.A Common Compatibility Index of Judgement Matrices[J].Journal of Southeast University(Natural Science Edition),2001,31(6):94-97. |
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| Authors: | Xu Zeshui Da Qingli |
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| Institution: | Xu Zeshui 1,2 Da Qingli 1 |
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| Abstract: | This paper first presents the transformation formulas of reciprocal judgement matrix and complementary judgement matrix, and then points out the relationship between the perfectly consistent reciprocal judgement matrix and the perfectly consistent complementary judgement matrix. Based on the characteristics of reciprocal judgement matrix and complementary judgement matrix, a common compatibility index of judgement matrices (reciprocal judgement matrices and complementary judgement matrices) and the concept of reciprocal weight matrix and complementary weight matrix are given. The compatibility and consistency of judgement matrices are studied in detail, and a criterion to measure the compatibility of judgement matrices is also provided. These results can help to improve the reasonability and effectiveness of decision, and thus have great practical application prospect in group decision making. Finally, a numerical example is given. |
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| Keywords: | judgement matrix compatibility consistency weight matrix |
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