引用本文:奚雷,丁松,徐宁,等.新信息优先原理下非等间距GM(1,1)模型优化研究[J].控制与决策,2019,34(10):2221-2228
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新信息优先原理下非等间距GM(1,1)模型优化研究
奚雷1,2, 丁松3, 徐宁4, 熊萍萍5
(1. 南京航空航天大学经济与管理学院,南京211106;2. 安徽科技学院管理学院,安徽滁州233100;3. 浙江财经大学经济学院,浙江杭州310018;4. 南京审计大学管理科学与工程学院,南京211815;5. 南京信息工程大学数学学院,南京210044)
摘要:
针对现实工程应用中存在非等间距序列问题,基于新信息优先原理提出非等间距GM(1,1)$优化模型.在对现有初始条件优化方法的缺陷进行分析的基础上,基于新信息优先原理,利用一阶累加生成序列的各分量加权和重构模型的初始条件,并利用各时点分量大小计算新旧信息间的权重分配比例,强化新信息对发展趋势的修正作用;在相对误差平方和最小准则下,给出时间参数的求解公式,进而构建优化模型.通过递增和递减两个类型实例研究,表明所提出优化模型能够充分利用新信息,预测精度优于其他初始条件改进模型.
关键词:  新信息优先  非等间距GM(1,1)模型  初始条件  优化
DOI:10.13195/j.kzyjc.2018.0163
分类号:N941.5
基金项目:国家自然科学基金项目(71901191,71771119,71701101,71701105);江苏省高校自然科学研究项目(16KJD120001);江苏省社科基金重点研究项目(16GLA001).
Research on optimization of non-equidistant GM(1,1) model based on the principle of new information priority
XI Lei1,2,DING Song3,XU Ning4,XIONG Ping-ping5
(1. College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;2. College of Management,Anhui Science and Technology University,Chuzhou 233100,China;3. School of Economics,Zhejiang University of Finance & Economics,Hangzhou310018,China;4. College of Management Science and Engineering,Nanjing Audit University,Nanjing 211815,China;5. College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)
Abstract:
Aiming at the non-equidistant problems, an optimized non-equidistant GM(1,1)$ model is designed based on the principle of new information priority. After analyzing the defects of previous optimized initial conditions, a new initial condition is designed by using the weighted sum of each component in 1-AGO sequence based on the principle of the new information priority. In order to show the modified effects of the new data points, the weight of each component in this newly proposed initial condition is calculated based on its value. Under the premise of minimizing the square sum of the relative error between the original series and the forecasting sequences, the solution to the newly generating parameter is presented. To verify the effectiveness of the novel model, two cases of increasing and decreasing sequences are conductd. The experimental results show that the optimized model can make full use of the new information, so as to achieve better forecasts than the previous modified models.
Key words:  new information priority  non-equidistant GM(1,1)$ model  initial condition  optimization.

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