联立灰色模型SGM(1,2)及其应用

SGM(1,2) and Its Application

灰色系统预测常用的模型有GM(1,1)、GM(1,N)、GM(N,1)等,这些模型的白化方程都是单一的常微分方程。然而客观世界在不断发展变化的同时,往往事物之间及因素之间相互制约、相互联系构成一个整体,变量之间是相互影响的,单一的微分方程有时不能很好地反映这种关系。文章提出一个新的联立灰色模型,给出了两个变量相互影响的联立灰色模型SGM(1,2)建立方法,实例表明联立灰色模型的精度比传统单一灰色模型有显著提高。

The commonly used models for grey system prediction are GM(1,1),GM(1,N),GM(N,1),etc.The whitening equations of these models are all single ordinary differential equations.However,as the objective world continues to develop and change,things and factors often restrict each other,interlinked together to form a whole,variables affecting each other,and sometimes the single differential equation can not reflect the relationship well.This paper proposes a new simultaneous grey model(SGM),giving a method to establish the SGM(1,2)with the interaction of two variables.The example shows that the precision of the simultaneous grey model is significantly improved compared with the traditional single grey model.