中国火灾最佳灰色回归组合预测模型

火灾现象具有随机性、模糊性,是个复杂的灰色系统行为。研究火灾发生的规律及发展趋势,具有实用价值。笔者给出最小二乘估计意义下的最佳组合预测模型的定义,并求得其权的公式和证明权的惟一性;用回归分析方法建立多个回归模型,并按3条标准即①回归指数大、②系统误差小、③模型精度高,选定最佳非线性回归模型;用灰色理论建立多个灰色模型,并按3条标准即①后验差比值小、②小误差概率大、③预测关联度大,选定最佳灰色模型;再将最佳回归模型与最佳灰色模型有机地结合起来建立中国火灾最佳灰色回归组合预测模型。组合预测模型综合利用前两者提供的不同的有用信息,改善了单一模型的局限性,提高了预测精度,减少了预测误差。组合模型预测中国年火灾起数处于动态增长过程。

Optimal Grey-regression Combinatorial Forecasting Model for Fire in China

Fire is a complex action of Grey system with random and fuzzy complexity. It is of practical value to study the rule of fire occurrence and its evolutional trend. Therefore, firstly the definition of optimal combinatorial forecasting model is given in the sense of least square estimate to find out the expression of weight of the above mentioned model and to prove it to be unique. Then the optimal nonlinear regression forecasting model is selected by establishing several regression models by means of regression analysis and in accordance with the following three standards, i.e. index of correlation, error of system, and precision of model. The optimal Grey forecasting model is selected by establishing several Grey models by means of Grey theory in accordance with following three standards, i.e. quotient of square error, probability of error, and forecasting relative degree. Finally an optimal combinatorial forecasting model for fire in China has been established through combining the Grey and regression models. The combinatorial forecasting model combines two sources of information together to improve and expand the corresponding field for Grey model & regression model making the results more accurate. It could forecast the occurrence of fire in China in a dynamic increase trend year after year.