A New DGM(1,1) Model with a Grey Parameter and Its Application

Abstract

In the DGM(1,1) model modeling process, the influencing factors are uncertain. But the solution of DGM(1,1) model with uncertain information is unique, which conflicts with the nonuniqueness principle of solution in grey theory. In view of this situation, this paper makes an in-depth analysis of the meaning of grey action quantity <i>β</i>2 in DGM(1,1) model and regards <i>β</i>2 as an interval grey number. The maximum possibility whitenization value is given to estimate the kernel of grey number, and the typical possibility function is constructed to describe the possibility of grey number taking different values. A new DGM(1,1) model with a grey parameter is then proposed, whose simulation results are interval grey numbers. The proposed model is compatible with the DGM(1,1) model in model structure and simulation results. Finally, the practical example results show the applicability and effectiveness of the proposed model.