模糊线性回归模型的最小二乘方法

针对自变量和因变量皆模糊的数据系统中的回归分析问题,为避免自变量退化成数值变量时可能引致的估计误差增大而带来的问题,提出系统中引入模糊调整项的回归模型的一般结构,并运用基于模糊数间完备距离的最小二乘法研究模型解析表达式;利用水平截集概念将模糊多元回归模型转化成两个传统回归模型,根据模糊数间距离采用最小二乘法得到参数估计,给出员工工作绩效评估的算例说明方法的有效性,并结合Bootstrap方法的应用,研究回归参数所具有的随机不确定性动态变化。

Distance-Based Least Squares Method for Fuzzy Linear Regression Models

A general structure of the fuzzy regression model with adjusted term is proposed to avoid the problems brought by the increase of estimates errors when the independent variables are degraded into numerical variables . T he least square method based on the complete distance is used to research the analytical expression .Firstly ,translate the fuzzy multiple linear regression model into two traditional regression models .Then ,estimate the parameters according to the distance by least‐square .An example applied to evaluate employees'performance is given to illustrate the effectiveness . We also analyze the uncertain dynamic changes of the regression parameters by bootstrap method .