一种强兼容性的灰色通用预测模型及其性质研究  

Researching on A Grey Common Prediction Modeling with Strong Compatibility and Its Properties

作　　者：曾波[1] 刘思峰[2] 曲学鑫 ZENG Bo LIU Si-feng QU Xue-xin(College of business planning, Chongqing Technology and Business University, Chongqing 400067, China College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing 400067, China)

机构地区：[1]重庆工商大学商务策划学院,重庆400067 [2]南京航空航天大学经济与管理学院,江苏南京210016 [3]重庆工商大学国家智能制造服务国际科技合作基地,重庆400067

出　　处：《中国管理科学》2017年第5期150-156,共7页Chinese Journal of Management Science

基　　金：国家自然科学基金资助项目(71271226);重庆市社科规划委托项目(2016WT37);重庆市教育科学规划课题(2012-GX-142);中国科协重大招标项目(2016ZCYJ06)

摘　　要：预测建模对象的复杂性导致了灰色模型形式的多样性与结构的互不兼容性,通过在灰色模型中引入因变量滞后项、线性修正项及常数修正项,构建了一种强兼容性的灰色通用预测模型(CGPM),证明了CGPM模型与多变量GM(1,N)模型与GM(0,N)模型及单变量GM(1,1)模型、DGM(1,1)模型及NDGM(1,1)模型的转换条件与等价性质,最后通过实例对CGPM模型的有效性进行了验证;研究成果对优化灰色模型结构、提高灰色模型通用性与普适性具有积极意义。The complicacy of predictive modeling object gives rise tO the diversity of form and mutual non-compatibility of structure of grey models. A grey common prediction modeling with powerful compatibility （CGPM） is established through putting the lagged item of dependent variable, corrective terms of linear and constant into grey model. The transformation conditions and equivalence properties between CGPM model and multivariable grey models which include GM（1, N） and GM（0, N） and single variable grey models including GM（1, 1）, DGM（1, 1） and NDGM（1, 1） are proved in this paper. The effectiveness of CGPM model is verified by some calculation examples. The study findings have some positive significance for optimizing the structure of grey model and improving the commonality and universality of grey model.

关 键 词：灰色理论 预测模型 强兼容性 模型转换 

分 类 号：N941.5[自然科学总论—系统科学]