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.
[1] Deng Julong. Control problem of grey systems[J]. System Control Letter, 1982, 1(5):288-294.
[2] Liu Sifeng, Lin Y. Grey system theory and applications[M]. Berlin Heidelberg:Springer-Verlag, 2010.
[3] Xia Min, Wong W K. A seasonal discrete grey forecasting model for fashion retailing[J].Knowledge-based Systems, 2014, 57:119-126.
[4] 姚天祥, 刘思峰, 党耀国. 初始值优化的离散灰色预测模型[J]. 系统工程与电子技术, 2009, 31(10):2394-2398.
[5] 戴文战. 基于函数基于函数cot(xα)变换及背景值优化的灰色建模[J]. 浙江大学学报(工学版), 2010, 44(7):1368-1372.
[6] Wei Yong, Zhang Yi. A criterion of comparing the function transformations to raise the smooth degree of grey modeling data[J]. The Journal of Grey System.2007, 19(1):91-98.
[7] 熊萍萍, 党耀国, 姚天祥,等. 灰色Verhulst模型背景值优化的建模方法研究[J]. 中国管理科学, 2012, 20(6):155-159.
[8] Wei Yong, Zhang Yi. An essential characteristic of the discrete function transformation to increase the smooth degree of data[J]. The Journal of Grey System, 2007, 19(3):293-300.
[9] Zeng Bo, Chen Guo, Liu Sifeng. A novel interval grey prediction model considering uncertain information[J]. Journal of the Franklin Institute, 2013,350(10):3400-3416.
[10] Xie Nainming, Liu Sifeng. Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model[J]. Journal of Systems Engineering and Electronics, 2015, 26(1):96-102.
[11] 曾波,刘思峰,孟伟. 具有主观取值倾向的离散灰数预测模型及其应用[J]. 控制与决策, 2012, 27(9):1359-1364.
[12] Xie Naiming, Liu Sifeng. Discrete grey forecasting model and its optimization[J]. Applied Mathematical Modeling, 2009,33(2):1173-1186.
[13] 曾波, 孟伟, 刘思峰,等. 面向灾害应急物资需求的灰色异构数据预测建模方法[J]. 中国管理科学, 2015, 23(8):85-91.
[14] 孟庆良, 何林, 朱慧明,等. 基于GM(1,1)模型的Kano质量要素分类动态预测方法[J]. 中国管理科学, 2015, 23(9):140-145.
[15] Liu Jun, Xiao Xinping. The relationship of discrete grey forecasting model DGM and GM(1,1) model[J]. Journal of Grey System, 2014, 26(4):14-31.
[16] Xie Naiming, Zhu Chaoyu, Zheng Jing. Expansion modeling of discrete grey model based on multi-factor information aggregation[J]. Journal of Systems Engineering and Electronics, 2014, 25(5):833-839.
[17] Xiao Xinping, Guo Huan, Mao Shuhua. The modeling mechanism, extension and optimization of grey GM(1,1) model[J]. Applied Mathematical Modeling, 2014, 38(5-6):1896-1910.
[18] Chen C I, Huang S J. The necessary and sufficient condition for GM(1,1) grey prediction model[J]. Applied Mathematics and Computation, 2013, 219(11):6152-6162.
[19] Zeng Bo, Li Chuan, Chen Guo,et al. Equivalency and unbiasedness of grey prediction models[J]. Journal of Systems Engineering and Electronics, 2015, 26(1):110-118.
[20] 肖新平, 毛树华. 灰预测与决策方法[M]. 北京:科学出版社, 2013.
[21] 郭晓君, 刘思峰, 杨英杰. 基于自忆性原理的多变量MGM(1,m)耦合系统模型构建及应用[J]. 中国管理科学, 2015, 23(11):113-118.
[22] 于志军, 杨善林,章政,等. 基于误差矫正的灰色神经网络股票收益率预测[J].中国管理科学,2015, 23(12):21-26.
