基于LR模糊数据的线性回归模型

Linear regression model based on the LR fuzzy numbers

LR模糊数据是实践中经常使用的由形状函数L及R、左右扩展及中心构成的模糊数.取值LR模糊数的随机变量称为模糊随机变量,其缺乏适宜的概率分布模型,导致模糊数据的线性回归模型缺乏显著性检验.文章基于Nther模糊随机变量线性回归分析工作,进一步给出LR模糊数据多元线性回归在δ2距离下的系数估计,并通过统计软件给出模型中非确定干扰变量的Bootstrap模拟分布.

LR fuzzy data is a kind of fuzzy number with the shape function of L and R, left and right extension, and the center. Fuzzy random variables are random variables with values of LR fuzzy numbers. It lacks the appropriate probability distribution model, which leads to the difficulties of the significance test for fuzzy data linear regression model. Based on Nather＇s work of the fuzzy linear regression with fuzzy random variables, we give linear regression model in which both input and output data are LR fuzzy numbers, and get the coefficient estimates with δ^2 distance considered. Then, we give the Bootstrap simulating distribution for the uncertain disturbance variable of fuzzy linear regression model by statistical software.