The characteristics analysis of SCGM(1,1) model and the new grey modeling methods

The system with partial unknown structure, parameters and characteristics is called a grey system. Grey system theory is a newly developed theory to deal with the problem of uncertainties in the case with “poor” information and has widely been used in many fields. The grey prediction SCGM(1,1) model has been used widely. In this paper, the characteristics of SCGM(1,1) model are systematically studied. Some new existing forms of SCGM(1,1) are derived including exponential form, α, β parameter form, scale form and recursive form. The parameter range suitable for SCGM(1,1) modeling has been studied based on strict proof. The prohibited area and the area not suitable or suitable for modeling of SCGM(1,1) model are divided clearly according to the developing coefficient a. Then, the discrete form of developing coefficient a is given. Based on the discrete form of developing coefficient a, a new grey modeling method avoiding complex matrix calculation is presented.