| 基于虚拟变量控制的GM(1,N)模型构建及其应用 |
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| 引用本文： | 丁松,党耀国,徐宁.基于虚拟变量控制的GM(1,N)模型构建及其应用[J].控制与决策,2018,33(2):309-315. |
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| 作者姓名： | 丁松 党耀国 徐宁 |
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| 作者单位： | 南京航空航天大学经济与管理学院,南京211106,南京航空航天大学经济与管理学院,南京211106,南京审计大学管理科学与工程学院,南京211815 |
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| 基金项目： | 国家自然科学基金项目(71371098, 71701024)；中央高校基本科研业务费专项资金项目(2017301)；江苏省普通高校研究生科研创新计划项目(KYZZ16_0153)；南京航空航天大学博士学位论文创新与创优基金项目(BCXJ16-09)；江苏省高校自然科学研究项目(16KJD120001)；江苏省社科基金重点研究项目(16GLA001). |
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| 摘 要： | 现实中系统行为特征序列常受到虚拟变量的影响,而此时传统GM(1,N)模型不能准确地描述系统特征的变化规律.将虚拟变量引入传统GM(1,N)模型的灰作用量,构建虚拟变量控制的GM(1,N)模型,讨论新模型的参数求解方法;鉴于背景值对模型精度有着重要影响,利用粒子群优化算法对含有插值系数的背景值进行优化求解;从两个角度提出虚拟变量有效性检验方法.最后,通过河南省农民人均收入预测案例表明,新模型能够准确描述虚拟变量影响下系统特征序列的未来变化趋势.
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| 关 键 词： | 灰色系统 GM(1 N) 虚拟变量 预测 |
Construction and application of GM(1,N) based on control of dummy variables |
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| DING Song,DANG Yao-guo and XU Ning.Construction and application of GM(1,N) based on control of dummy variables[J].Control and Decision,2018,33(2):309-315. |
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| Authors: | DING Song DANG Yao-guo and XU Ning |
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| Affiliation: | College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China,College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China and College of Management Science and Engineering,Nanjing Audit University,Nanjing 211815,China |
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| Abstract: | To solve the problems that the traditional GM(1,N) model can not describe precisely the changing patterns of the system behavior characteristic variables influenced by the dummy variables in the real life, the dummy variables are introduced into the grey acting term of the conventional GM(1,N) model, and the novel GM(1,N) model is built with discussing the estimating methods of the parameters. Due to the great effect of the background value on the precision of modeling, the interpolated coefficient of the background value is optimized by using the PSO algorithm. The test methods of validity are proposed from two perspectives. Finally, the per capital income of farmers in Henan province is simulated and predicted, which shows that the proposed model can effectively describes the future trend of system change influenced by dummy variables. |
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