| 基于分数阶累加的离散灰色模型 |
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| 引用本文： | 吴利丰,刘思峰,姚立根. 基于分数阶累加的离散灰色模型[J]. 系统工程理论与实践, 2014, 34(7): 1822-1827. DOI: 10.12011/1000-6788(2014)7-1822 |
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| 作者姓名： | 吴利丰 刘思峰 姚立根 |
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| 作者单位： | 1. 南京航空航天大学 经济与管理学院, 南京 210016;2. 河北工程大学 经济管理学院, 邯郸 056038 |
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| 基金项目： | 国家社科基金重点项目(12AZD102);国家自然科学基金(71171113,71111130211);南京航空航天大学引进人才基金(1009YAH14003) |
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| 摘 要： | 针对灰色预测模型为什么适用于“小样本”建模的问题进行了研究. 以离散灰色模型为例，利用最小二乘问题解的扰动理论证明了灰色一阶累加方法在扰动相等的情况下，原始序列样本量较大，解的扰动界较大； 样本量较小，解的扰动界较小. 为了使离散灰色模型解的扰动界变小，本文提出了分数阶累加离散灰色模型. 实例说明分数阶累加离散灰色模型的实用性.
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| 关 键 词： | 灰色系统 离散灰色模型 小样本 扰动分析 |
| 收稿时间： | 2012-09-04 |
Discrete grey model based on fractional order accumulate |
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| WU Li-feng,LIU Si-feng,YAO Li-gen. Discrete grey model based on fractional order accumulate[J]. Systems Engineering —Theory & Practice, 2014, 34(7): 1822-1827. DOI: 10.12011/1000-6788(2014)7-1822 |
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| Authors: | WU Li-feng LIU Si-feng YAO Li-gen |
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| Affiliation: | 1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;2. School of Economics and Management, Hebei University of Engineering, Handan 056038, China |
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| Abstract: | Why grey model is suitable for small sample is explained. Take discrete grey model as an example, based on matrix perturbation theory, we prove that the larger sample, the bigger perturbation bound and the smaller sample, the smaller perturbation bound under the equal perturbation when we use the traditional grey first order accumulate. The fractional order accumulate grey model is defined in order to reduce perturbation bound and its availability and practicality are verified by an example. |
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| Keywords: | grey system discrete grey model small sample perturbation analysis |
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