具有交互效应的多变量GM(1,$textbf{N}$)模型

针对一类具有交互效应的小样本系统建模问题,将相关因素序列的交叉项引入经典GM(1,N)模型的灰色作用量,构建交互效应GM(1,N)模型及其派生模型,以反映不同输入变量之间的交互效应对系统特征变量的影响,并通过实例验证交互效应GM(1,N)模型的有效性.结果表明:当相关因素序列的交互作用系数为零时,交互效应GM(1,N)模型退化为经典GM(1,N)模型;对于具有交互效应的系统建模问题,交互效应模型较经典模型具有更高的模拟和预测精度.

Multivariable GM(1,$textbf{N

To solve the modeling problem of the small sample system with interaction effects, the GM(1,N) model with interaction effects and its derived model are constructed by introducing cross terms into the grey acting term of the classical GM$(1,n)$ model. Thus the impacts of interaction effects between different input variables on systems'' characteristic variables can be effectively reflected. An actual example is studied to illustrate the effectiveness of the GM(1,N) model with interaction effects. The results showthat the GM(1,N) model with interaction effects degenerate into the classical model when the interaction coefficients between related factors are zero. The model with interaction effects has higher simulation and prediction precision than that of classical model for the systems modeling problem with interaction effects.