含Flat Fuzzy参数的回归预测模型的探讨

在现实世界中,有这样一类不确定的现象,即事件发生与否是确定的,但其本身是不分明的。对此,如何进行回归分析,统计预测呢?这是一个具有广阔研究前景的领域。文[1]讨论了一类不分明自回归预测模型,本文则在此基础上讨论含flat fuzzy参数的线性回归预测模型。同时把这类模型推广到时间序列中去,建立了Fuzzy自回归模型。笔者运用了flat fuzzy数的有关性质,把确定flat fuzzy参数A_j,归结为求解含参变量的线性规划问题,从而避免了用经典最小二乘法时,参数A_j不可微的麻烦,成功地确定了A_j,建立了回归预测模型,这就为回归统计预测,提供了另一种方法。

STUDY OF THE REGRESSION FORECASTING MODEL WITH FLAT FUZZY PARAMETERS

There is such a kind of uncertain phenomenon in the realistic world, that is, the occur-rence or non-occurrence is determinate, but the event itself is unclear. Therefore, it remainsan extensive tresearch field how to take up regression analysis and statistical forecasting. ThePaper [1] discussed a kind of nondistinct self-regression forecasting model, on which thispaper is to discuss the linear regression forecasting model with flat fuzzy parameters, to de-velop this model into the time series and to establish fuzzzy self-regression forecasting mod-el. After applying some properties of flat fuzzy, the writer inducts the determination of re-gression parameters into the solution of linear programming problem with parameter vari-ables, which avoids the troubles of regerssion parameter A_i non-differentiable by the classi-cal least square method and succeeds in determining the regression forecasting model whichprovides a new method for regression statistical forecasting.