Modeling solution and properties research on the General GM(1,1) model

Abstract

Discrete GM(1,1) model solves the bias defect in homogeneous exponential fitting using GM (1,1) model. General GM(1,1) model solves the conversion problem of the original equation between differential form and differential form, and can effectively profile GM(1,1) model and Discrete GM(1,1) model. But, the modeling mechanism, solution approach and lots of good properties about General GM(1,1) model do not take in-depth studying. So that, we research the mechanism of the General GM(1,1) modeling and three solution approaches about the stepwise ratio including the fitting approach of initial information, the fitting approach of new information and the overall error minimization approach in this paper. Then, we further detailed analysis some important properties such as the general nature, the fitting optimization property, the homogeneous exponential property and the unbiased property to fit homogeneous exponent. At last, the feasibility and the optimization properties are confirmed through an real example. Then, General GM(1,1) model and Grey Prediction Theory could be effetely improved and perfected for this article.