Four basic models of GM(1, 1) and their suitable sequences

Purpose – The purpose of this paper is to provide a foundational reference and practical guidance for modelling small and poor data with incomplete information. Design/methodology/approach – The definitions of four basic models of GM(1, 1), such as Even Grey Model (EGM), Original Difference Grey Model (ODGM), Even Difference Grey Model (EDGM) and Discrete Grey Model (DGM), are put forward. The properties and characteristics of different models are studied and their equivalence are proved. The suitable sequences of different models are studied by simulation and analysis with homogeneous exponential sequences, nonhomogeneous exponential increasing sequences and vibration sequences. Findings – The main conclusions have been obtained as follows: first, the three discrete models of ODGM, EDGM and DGM are suitable for homogeneous exponential sequences or sequences which close to a homogeneous exponential sequence; and second the EGM are suitable for nonhomogeneous exponential increasing sequences and vibration ...

[1]  Yi Lin,et al.  A SYSTEMIC ANALYSIS WITH DATA (II) , 2000 .

[2]  Robert Vallée,et al.  Grey Information: Theory and Practical Applications , 2008 .

[3]  Wang Yinao.  An Extended Step by Step Optimum Direct Modeling Method of GM(1,1) , 2003 .

[4]  Liu Si-feng,et al.  An optimal GM(1,1) based on the discrete function with exponential law , 2008 .

[5]  Lotfi A. Zadeh,et al.  Soft computing and fuzzy logic , 1994, IEEE Software.

[6]  Alex M. Andrew.  Why the world is grey , 2011, Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services.

[7]  Liu Si-feng,et al.  Discrete GM(1,1) and Mechanism of Grey Forecasting Model , 2005 .

[8]  Jose L. Salmeron,et al.  Modelling grey uncertainty with Fuzzy Grey Cognitive Maps , 2010, Expert Syst. Appl..

[9]  Liu Si-feng,et al.  The GM models that x(n) be taken as initial value , 2004 .

[10]  Camelia Delcea,et al.  Complete analysis of bankruptcy syndrome using grey systems theory , 2011, Grey Syst. Theory Appl..

[11]  Yi Lin,et al.  Grey Systems: Theory and Applications , 2010 .

[12]  Jeffrey Forrest,et al.  Generalized discrete GM (1, 1) model , 2011, Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services.

[13]  Yong-Huang Lin,et al.  Novel high-precision grey forecasting model , 2007 .

[14]  Sifeng Liu,et al.  Grey Control Systems , 2010 .

[15]  Liu Si,et al.  Optimum Time Response Sequence for GM(1,1) , 2003 .

[16]  Luo Youxin.  Non-equidistant step by step optimum new information GM(1,1) and its application , 2010 .

[17]  Tan Guan-jun,et al.  The Structure Method and Application of Background Value in Grey System GM(1,1) Model (II) , 2000 .

[18]  Jie Cui,et al.  Study on parameters characteristics of NGM(1,1,k) prediction model with multiplication transformation , 2011, Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services.

[19]  Liu Si-feng,et al.  On astray of complicated model for uncertain system , 2011 .

[20]  Wang Zheng-xin.  The Optimization of Background Value in Non-Equidistant GM(1,1) Model , 2008 .

[21]  Liu Si-feng.  Indirect generating grey model based on particle swarm optimization algorithm , 2010 .

[22]  Si-feng Liu,et al.  Optimization of Background Value in GM(1,1) Model , 2008 .

[23]  Sifeng Liu,et al.  Study on parameters characteristics of NGM(1,1,k) prediction model with multiplication transformation , 2011 .

[24]  L. Junfeng,et al.  Modeling Research on Non-equidistance GM(1,1) Model , 2005 .

[25]  Liu Si-fen,et al.  The Range Suitable for GM (1,1) , 2000 .

[26]  Liu Si-feng,et al.  Research on Extension of Discrete Grey Model and Its Optimize Formula , 2006 .

[27]  Xinhai Kong,et al.  A kind of universal constructor method for buffer operator , 2011, Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services.

[28]  Yong Wei,et al.  A kind of universal constructor method for buffer operator , 2011 .

[29]  Yi Lin,et al.  Grey Information - Theory and Practical Applications , 2005, Advanced Information and Knowledge Processing.

[30]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[31]  Liu Si-feng.  Sequence of strengthening buffer operator and its application based on fixed point , 2007 .