系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2014年
10期
2628~2636
,共null页
模糊多元线性回归 最小二乘法 模糊结构元 三角模糊数 E-距离
模糊多元線性迴歸 最小二乘法 模糊結構元 三角模糊數 E-距離
모호다원선성회귀 최소이승법 모호결구원 삼각모호수 E-거리
fuzzy multiple linear regression; least-squares approach; fuzzy structured element; triangular fuzzy numbers; E-distance
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．
針對繫數為模糊數的多元線性迴歸模型，運用基于模糊結構元理論的最小二乘法，研究模型的解析錶達式．首先運用模糊結構元方法定義瞭模糊數距離公式，該公式與文[1]給齣的距離公式在一定條件下等價，但避免瞭後者因區間運算而帶來的不便．對模糊參數用結構元理論錶示，得到瞭模型的解析錶達式．再根據定義的距離公式採用最小二乘法得到瞭估計模糊參數的方法．根據該方法得到繫數為LR-型模糊數的迴歸模型．最後給齣一箇應用算例，說明本文方法的簡便性．
침대계수위모호수적다원선성회귀모형，운용기우모호결구원이론적최소이승법，연구모형적해석표체식．수선운용모호결구원방법정의료모호수거리공식，해공식여문[1]급출적거리공식재일정조건하등개，단피면료후자인구간운산이대래적불편．대모호삼수용결구원이론표시，득도료모형적해석표체식．재근거정의적거리공식채용최소이승법득도료고계모호삼수적방법．근거해방법득도계수위LR-형모호수적회귀모형．최후급출일개응용산례，설명본문방법적간편성．
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.
