小样本非等间距灰色预测模型建模及其应用研究

项目名称： 小样本非等间距灰色预测模型建模及其应用研究

项目编号： No.71301061

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 管理科学

项目作者： 王育红

作者单位： 江南大学

项目金额： 23万元

中文摘要： 随着经济发展与社会生产力水平的提高，人们常常会遇到小样本非等间距序列的预测问题；然而面对这样的预测问题，还缺乏有效的方法和工具。本项目以灰色系统理论为基础，研究小样本非等间距灰色预测模型的构建和应用问题。将未知参数引入非等间距序列算子的构造之中，并研究未知参数的量化值与算子作用强度之间的定量关系；利用均方偏差最小化的分形插值算法，把原始的非等间距序列生成等间距序列，研究垂直压缩因子的取值变化对于非等间距灰色预测模型精度的影响幅度大小；在对非等间距灰色幂模型的构造、参数估计与优化的过程中，针对具有周期波动性和多数据特征的非等间距序列，研究非等间距周期波动幂模型、非等间距多数据幂模型，通过智能优化算法确定模型中的未知参数，剖析模型蕴含的特征；最后应用本项目中提出的理论模型和方法，对食品安全风险进行预警分析，以检验和修正本项目提出的理论和方法，为政府相关部门进行科学决策提供较为合理的支持。

中文关键词： 非等区间；小样本；灰色预测模型；灰色系统；

英文摘要： People often meet such a problem as prediction for sequence of small sample size and unequal interval with development of economics and improvement of productivity. There are still not sufficient methods and tools to face such questions. In this project, construction and application for grey prediction model with small sample size and unequal interval based on grey systems theory. Unkonwn parameters are added into construction of grey sequence operators. Also the relationship between the quantitative values of unknown parameters and the degree of strength on sequences. Some original sequences with unequal interval could be generated into some new sequences with equal interval for applying fractal interpolation algorithm with minimum of mean-square deviation. The impact of vertical compression factor on precion of grey prediction models with unequal interval. Construction, parameter estimaions and optimized grey models are studied. Some cyclical fluctuation in power models and multi=data power models are also constructed according to the individual characteristics. Some parameters are estimated according to some intelligental optimized algorithms. Finally, modles and some other methods presented in the project are used for early-warning in food safety risk. Then we could check and modify some theoritical mehtods.

英文关键词： unequal interval；small sample size；grey prediction；grey system；