Research on ill-conditioned problem and modeling precision in GM(1,1) model

To solve the ill-conditioned problem and the modeling precision in grey prediction control GM(1,1) model, a new simple and effective method is presented. This method is based on multiple transformation to original series and center parallel moving transformation to AGO series, that is, a new grey optimization model based on affine transformation is proposed. Firstly, the parameter relationships and properties of the new model are discussed. Secondly, Based on the condition number and the modeling precision, a multi-objective optimization model is set up. By solving the model and choosing coefficients M and p, the condition number of coefficient matrix can be controlled, meanwhile, the prediction accuracy of the original grey model is improved. Finally, we use an application example for our case study to test the efficiency and accuracy of the proposed method.