| 偏序集理论在数据包络分析中的应用研究 |
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| 引用本文： | 马占新,唐焕文,戴仰山.偏序集理论在数据包络分析中的应用研究[J].系统工程学报,2002,17(1):19-25. |
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| 作者姓名： | 马占新 唐焕文 戴仰山 |
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| 作者单位： | 1. 哈尔滨工程大学船舶与海洋工程系,哈尔滨,150001
2. 大连理工大学管理科学与工程研究所,大连,116024 |
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| 摘 要： | DEA有效单元与偏序集的极大元之间关系密切，从偏序集的理论出发刻画了种典型的DEA模型所描述的DEA有效单元的本质特征，并就C^2R，C^2GS^2模型分析了DEA有效前沿面的构成，证明了可能集中相以圾效点与偏序集的极大元之间的一一对应关系，进而对DEA有效性的含义，DEA模型选取的基本原则等问题人出了基于偏序集理论的解释，同时，讨论了可能集结构变化对DEA有铲性的影响，给出了刻画各可能集间关系的一些结论，并就这些理论的的进一步应用和发展提出了一些建议和设想。
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| 关 键 词： | 数据包络分析 Pareto有效解 生产可能集 偏序集理论 运筹学 |
| 文章编号： | 1000-5781(2002)01-0019-07 |
| 修稿时间： | 2000年5月11日 |
Using theory of partially ordered sets to study data envelopment analysis |
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| MA Zhan-xin ,TANG Huan-wen ,DAI Yang-shan.Using theory of partially ordered sets to study data envelopment analysis[J].Journal of Systems Engineering,2002,17(1):19-25. |
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| Authors: | MA Zhan-xin TANG Huan-wen DAI Yang-shan |
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| Institution: | MA Zhan-xin 1,TANG Huan-wen 2,DAI Yang-shan 1 |
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| Abstract: | It has close relationship between an efficient unit and a maximum element. On the basis of the theory of partially ordered sets, this paper gives some characteristic properties of effective units in several DEA models and analyses the structure of fronters in C 2R, C 2GS 2 models, then proves exiting the one to one correspondence between an effective point and a maximum element. At the same time, the meaning of DEA efficiency is explained and a basic rule of selecting models is provided. In addition, the effects upon DEA efficiency due to the structure change of possible productive collections are discussed and some results are given. Finally, some suggestions for future research are provided. |
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| Keywords: | data envelopment analysis partially ordered set DEA efficiency Pareto effective solution possible productive collection |
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