基于GM(0,N)模型的三元区间数序列预测

Prediction of ternary interval number sequence based on GM(0, N) model

在工程和经济领域,很多数据序列具有很强的振荡性,这些振荡序列用区间数表示将包含更多信息.三元区间数不仅包含系统特征的上下界,还在中间增加一个偏好值,对三元区间数序列的预测研究具有很好的应用价值.为了使灰色模型GM(0, N)能够直接对三元区间数序列建模,改进了GM(0, N)模型方程的参数设置,将整体贡献系数和滞后项系数取为精确数,而将线性修正项系数和补偿系数设为三元区间数,从而对三元区间数的不同界点进行线性修正和补偿.进一步,为了提高对振荡序列的预测精度,结合马尔科夫预测和序列转换方法对模型的预测序列进行修正.通过对我国用电量和社会消费品零售总额的预测,表明了所提出的三元区间数多变量灰色模型比单变量灰色模型和区间数序列转换为精确数序列再预测的方法效果更好.

In the field of engineering and economics, many data sequences have strong oscillation. These oscillating sequences, represented by interval numbers, will contain more information. The ternary interval number not only contains the upper and lower bounds of the system characteristics, but also contains a preference value. It has a good application value to study the prediction of the sequence of ternary interval numbers. In order to make the multivariable grey model GM(0, N) be able to directly model the ternary interval number sequence, the parameter setting of the GM(0, N) model equation is improved. The global contribution coefficient and lag coefficient are taken as the exact number. The linear correction term coefficient and compensation coefficient are set as the ternary interval numbers to compensate the different boundary points of the ternary interval number. Furthermore, to improve the prediction accuracy of the oscillatory sequence, the prediction sequence of the model is modified with the Markov prediction and sequence transformation method. By forecasting China’s electricity consumption and total retail sales of consumer goods, the comparison results show that the ternary interval number multivariate grey model presented in the paper is better than the single variable grey model and the method of forecasting after converting interval number series into exact number series.