On the new model system and framework of grey system theory

Abstract

The basic framework of grey system theory initiated by Professor Julong Deng, the founder of grey system theory, is introduced here. The most often used new thinking, methods, and models of grey system theory are presented in this paper, such as algorithm rules of grey numbers based on the “Kernel” and the degree of greyness of grey numbers, the concept of the general grey number, the synthesis axiom of degree of greyness of grey numbers and their operations; the most used weakening buffer operator which has good properties for the general form of buffer operator of grey sequence operator; the four basic models of GM(1,1), such as Even Grey Model (EGM), Original Difference Grey Model (ODGM), Even Difference Grey Model (EDGM), Discrete Grey Model (DGM), the suitable sequence type of each basic model, and the suitable range of the most often used grey forecasting model; the absolute degree of grey incidence, the relative degree of grey incidence, the synthetic degree of grey incidence, the similarity degree of grey incidence, the closeness degree of grey incidence and the three dimensions absolute degree of grey incidence in grey incidence analysis models; the grey cluster model based on mixed center-point and end-point mixed triangular whitenization weight functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision model; grey game model, grey input-output model of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. The reader could know the general picture of research and the developing trends of grey system theory from this paper, and a new model system and framework of grey system theory will have been presented at last.