Modeling mechanism and extension of GM (1,1)

作     者：Xinping Xiao Yichen Hu Huan Guo 

作者机构：School of ScienceWuhan University of Technology School of EconomicsWuhan University of Technology 

出 版 物：《Journal of Systems Engineering and Electronics》 (系统工程与电子技术（英文版）)

年 卷 期：2013年第24卷第3期

页      面：445-453页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070102[理学-计算数学] 071101[理学-系统理论] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(70971103) the Specialized Research Fund for the Doctora Program of Higher Education(20120143110001) 

主　　题：GM (1,1) matrix analysis GGM (1,1) model parameter modeling mechanism. 

摘      要：Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study the modeling mechanism of GM （1,1）, which decomposes the modeling data matrix into raw data transformation matrix, accumulated generating operation matrix and background value selection matrix. The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM （1,1）. Finally, the paper proposes a generalization grey model GGM （1,1）, which is a extended form of GM （1,1） and also a unified form of model GM （1,1）, model GM （1,1,α）, stage grey model, hopping grey model, generalized accumulated model, strengthening operator model, weakening operator model and unequal interval model. And the theory and practical significance of the extended model is analyzed.