基于多目标规划法的模糊线性回归分析

讨论输入、输出均为模糊数,回归系数为实数时的模糊线性回归分析。由于模糊最小二乘线性回归容易受异常值的影响,而最小一乘法能有效地降低回归模型的误差。为此,基于最小一乘法,建立多目标规划模型并将其转化为非线性规划问题进行求解,从而实现模糊线性回归模型的参数估计。最后,结合一个数值实例,验证和比较该方法的合理性和优越性。

A Multi-objective Programming Approach to Fuzzy Linear Regression Analysis

This paper discusses the fuzzy linear regression analysis with fuzzy inputs-outputs and real regression coefficients.With the view that fuzzy least square linear regression is vulnerable to outliers,and the least absolute method can effectively reduce errors in regression model,we build a multi-objective programming model and solve it by transforming into a nonlinear programming problem based on least absolute,in order to estimate parameter in fuzzy linear regression model.Also,we illustrate the rationality and superiority of the proposed approach by a numerical example.