| 模糊多目标半定规划 |
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| 引用本文： | 刘睿,张可村.模糊多目标半定规划[J].数学研究及应用,2010,30(4):599-609. |
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| 作者姓名： | 刘睿 张可村 |
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| 作者单位： | 西安航空技术高等专科学校基础部, 陕西 西安 710000; 中国航天时代电子公司第七七一研究所, 陕西 西安 710000;西安交通大学数学系, 陕西 西安 710049 |
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| 基金项目： | 国家自然科学基金(Grant No.10671057). |
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| 摘 要： | This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.
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| 关 键 词： | fuzzy multi-objective semi-definite programming membership function optimality efficient solution efficient solution optimality condition. |
| 收稿时间： | 2008/6/14 0:00:00 |
| 修稿时间： | 2009/9/15 0:00:00 |
Fuzzy Multi-Objective Semi-Definition Programming |
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| Rui LIU and Ke Cun ZHANG.Fuzzy Multi-Objective Semi-Definition Programming[J].Journal of Mathematical Research with Applications,2010,30(4):599-609. |
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| Authors: | Rui LIU and Ke Cun ZHANG |
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| Institution: | 1. Department of Basic, Xi'an Aerotechnical College, Shaanxi 710000, P. R. China;China Aerospace Times Electronics Corporation No.771 Research Institute Shaanxi 710000, P. R. China
2. Department of Mathematics, Xi'an Jiaotong University, Shaanxi 710049, P. R. China |
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| Abstract: | This paper first applies the fuzzy set theory to multi-objective semi-definite programming (MSDP), and proposes the fuzzy multi-objective semi-definite programming (FMSDP) model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation. |
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| Keywords: | fuzzy multi-objective semi-definite programming membership function optimality efficient solution efficient solution optimality condition |
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