| 模糊规划的对偶理论 |
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| 引用本文： | 张成,杨万才.模糊规划的对偶理论[J].辽宁师范大学学报(自然科学版),2005,28(1):1-6. |
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| 作者姓名： | 张成 杨万才 |
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| 作者单位： | 1. 大连大学,信息工程学院,辽宁,大连,116622
2. 河南科技大学,数理系,河南,洛阳,471003 |
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| 基金项目： | 辽宁省高校“信息科学与工程”重点实验室资助项目 |
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| 摘 要： | 建立了有关凸模糊映射的微分理论：利用凸模糊映射的微分理论研究极值问题，得到凸模糊映射取得极值的充分／必要条件；讨论模糊意义下的鞍点与极小极大定理，并与模糊规划的Lagrange对偶联系起来．最后，建立了凸模糊规划的Lagrange对偶和KKT条件，并将其结果应用到模糊线性规划与模糊二次规划的研究中．
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| 关 键 词： | 对偶理论 模糊映射 极小极大定理 鞍点 微分 极值 模糊规划 理论研究 模糊线性规划 二次规划 |
| 文章编号： | 1000-1735(2005)01-0001-06 |
| 修稿时间： | 2004年7月20日 |
Duality Theory of Fuzzy Programming |
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| ZHANGCheng,YANG Wan-cai.Duality Theory of Fuzzy Programming[J].Journal of Liaoning Normal University(Natural Science Edition),2005,28(1):1-6. |
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| Authors: | ZHANGCheng YANG Wan-cai |
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| Abstract: | A differential theory of convex fuzzy mapping is established in this paper. We first study the fuzzy extremum problems. The problems of minimizing and maximizing a convex fuzzy mapping are considered, and the necessary and/or sufficient optimality conditions are developed. We discuss the concept of saddle-points and minimax theorems under fuzzy environment. The results obtained are used to the Lagrangian dual of fuzzy programming. Lagrangian dual and KKT conditions for convex fuzzy programming are derived. Furtheromore, the above results are applied to fuzzy linear programming and fuzzy quadratic programming. |
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| Keywords: | fuzzy numbers convex fuzzy mappings subdifferential of convex fuzzy mapping fuzzy saddle-points convex fuzzy programming fuzzy Lagrangian dual KKT conditions |
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