Abstract: In this paper, the modeling and prediction problem of non-negative decreasing sequence are considered. Considering that a grey action will develop and change with the change of the time and space, the grey action is approximately regarded as a linear function of time to construct a GOM(1,1) model with grey action optimization. The optimal background value of GOM(1,1) model is derived by integration based on the non-homogeneous exponential characteristics of the data series of the grey prediction model. Based on the principle of minimum square sum of mean relative error between an original sequence and a simulated sequence, the optimal time response function expression was determined, and the improved algorithm of complete GOM(1,1) model was finally formed. Finally, the effectiveness and practicability of the improved model are verified by an application example.

Key words: GOM(1,1) model, grey action quantity, the background value, time response function