基于结构元理论的模糊多元线性回归模型

针对系数为模糊数的多元线性回归模型， 运用基于模糊结构元理论的最小二乘法， 研究模型的解析表达式. 首先运用模糊结构元方法定义了模糊数距离公式， 该公式与文1]给出的距离公式在一定条件下等价， 但避 免了后者因区间运算而带来的不便. 对模糊参数用结构元理论表示， 得到了模型的解析表达式. 再根据 定义的距离公式采用最小二乘法得到了估计模糊参数的方法. 根据该方法得到系数为LR-型模糊数的回归模型. 最后给出一个应用算例， 说明本文方法的简便性.

An approach to fuzzy multiple linear regression model based on the structured element theory

For multiple linear regression model which coefficients are fuzzy numbers, this paper uses least-squares approach based on fuzzy structured element theory to study analytical expression of the model. First, a new distance formula of fuzzy numbers is defined using structured element method, and also proved equivalent with one given by the paper 1] under certain conditions. But it can avoid the inconvenience of the latter caused by interval arithmetic. Fuzzy parameters are expressed by the structured element and analytical expression of fuzzy linear regression model is provided. Then we give a parameter estimation method for the model whose fuzzy parameters are LR-type fuzzy numbers. At last, an application example is presented in order to illustrate the simplification of the proposed method.