The common models used for grey system predictions include the GM(1, 1), the GM(1, N),the GM(N, 1), and so on, but their whitening equations are all single ordinary differential equations.However, objects and factors ...The common models used for grey system predictions include the GM(1, 1), the GM(1, N),the GM(N, 1), and so on, but their whitening equations are all single ordinary differential equations.However, objects and factors generally form a whole through mutual restrictions and connections when the objective world is developing and changing continuously. In other words, variables affect each other. The relationship can’t be properly reflected by the single differential equation. Therefore, the paper proposes a novel simultaneous grey model. The paper gives a modeling method of simultaneous grey model SGM(1, 2) with 2 interactive variables. The example proves that the simultaneous grey model has high precision and improves the precision significantly compared with the conventional single grey model. The new method proposed enriches the grey modeling method system and has important significance for the in-depth study, popularization and application of grey models.展开更多
基金Supported by the National Natural Science Foundation of China (11401418)。
文摘The common models used for grey system predictions include the GM(1, 1), the GM(1, N),the GM(N, 1), and so on, but their whitening equations are all single ordinary differential equations.However, objects and factors generally form a whole through mutual restrictions and connections when the objective world is developing and changing continuously. In other words, variables affect each other. The relationship can’t be properly reflected by the single differential equation. Therefore, the paper proposes a novel simultaneous grey model. The paper gives a modeling method of simultaneous grey model SGM(1, 2) with 2 interactive variables. The example proves that the simultaneous grey model has high precision and improves the precision significantly compared with the conventional single grey model. The new method proposed enriches the grey modeling method system and has important significance for the in-depth study, popularization and application of grey models.
