模糊线性回归预测

Fuzzy Linear Regression Prediction

为了解决带有模糊信息的动态预测问题 ,在已有的线性回归预测法的基础上 ,提出了模糊线性回归预测的模型 .模型的确定在于模糊系数的确定 ,模糊系数为对称三角模糊数 ,为此给出了描述对称三角模糊数近似程度的拟合度的定义及其表达式 .借助于对称三角模糊数以截集表示的一对函数 ,给出了对称模糊的模糊度的定义及其表达式 ,给出了确定模糊系数的准则 :对于事先指定的标准拟合度 ,要求在每个方程估计值的拟合度都不小于标准拟合度的约束条件下 ,使得模糊系数的综合模糊度达到最小 ,于是模糊系数的确定问题可转化为求解线性规划问题 .实例表明 :该模型具有很高的精度 .

The dynamic prediction problem with fuzzy information is solved by using the linear regression prediction method. This involves the determination of fuzzy coefficients which are symmetric triangular fuzzy numbers and the definition of fitness. Expressions are given to describe the closeness of the estimated value and observed value of the equation for two symmetric triangular fuzzy numbers. The solution is expressed in term of a pair of functions expressed in cutset for symmetric triangular fuzzy numbers. More specifically, fuzzy coefficients are minimized under the restrictive condition that the fitness of the estimated value of each equation is not less than the predesignated fitness, while determination of fuzzy coefficients is reduced to solving a linear planning problem.Examples show that the model can yield results with very high accuracy.