基于多目标规划法的模糊线性回归分析

A Multi-objective Programming Approach to Fuzzy Linear Regression Analysis

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。

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.