基于可能性均值-方差距离的模糊最小一乘回归模型
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摘要
文章针对自变量的系数和输出因变量是模糊数的模糊线性回归模型,引入模糊数的可能性均值和方差,构建模糊数的可能性均值-方差距离测度。借助于最小一乘法原理,给出了使得可能性均值-方差距离误差达到最小的回归系数估计值的线性规划模型。最后给出实例说明了方法的有效性和可行性。
Aiming at the fuzzy linear regression model whose coefficient of independent variable and output dependent variable are fuzzy numbers, this paper constructs fuzzy number's possibilistic mean-variance distance measurement. With the aid of the least absolute principle, the paper presents a linear programming model for the estimation of the regression coefficient with the minimum possibilistic mean-variance distance error. Finally the paper uses two examples of symmetric and asymmetric triangular fuzzy numbers to illustrate the effectiveness and feasibility of the proposed method.
Aiming at the fuzzy linear regression model whose coefficient of independent variable and output dependent variable are fuzzy numbers, this paper constructs fuzzy number's possibilistic mean-variance distance measurement. With the aid of the least absolute principle, the paper presents a linear programming model for the estimation of the regression coefficient with the minimum possibilistic mean-variance distance error. Finally the paper uses two examples of symmetric and asymmetric triangular fuzzy numbers to illustrate the effectiveness and feasibility of the proposed method.
引文
[1]Tanaka H,Uejima S,Asai K.Linear Regression Analysis With FuzzyModel[J].IEEE Transactions on Systems Man,and Cybernetics,1982,(12).
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[3]李俊红,曾文艺.基于梯形模糊数的模糊最小一乘回归模型[J].系统工程理论与实践,2015,35(6).
[4]彭宇文,郭莉莎,毛超.基于改进模拟退火算法的模糊回归参数估计[J].统计与决策,2014,(1).
[5]岳立柱.系数为一般模糊数的多元线性回归模型[J].统计与决策,2015,(3).
[6]Carlsson C,Fullér R.On Possibilistic Mean Valueand Variance of Fuzzy Numbers[J].Fuzzy Sets andSystems,2001,(122).
[7]Nasrabad M M.Narsabad E.A Mathematical-progrm-ming Approacg to Fuzzy Linear Regression Analysis[J].Applied Mathematics and Computation,2004,(155).
[8]Coppia R,Urso P D,Giordani P,et al.Least SquaresEstimation of a Linear Regression Model With LRFuzzy Response[J].Computational Statistics&DataAnalysis,2006,(51).
[9]黄华,易正俊.修正的模糊最小一乘线性回归[J].模糊系统与数学,2012,26(1).
[2]任燕,郭嗣琮.基于结构元最小二乘序的模糊线性回归[J].模糊系统与数学,2015,29(1).
[3]李俊红,曾文艺.基于梯形模糊数的模糊最小一乘回归模型[J].系统工程理论与实践,2015,35(6).
[4]彭宇文,郭莉莎,毛超.基于改进模拟退火算法的模糊回归参数估计[J].统计与决策,2014,(1).
[5]岳立柱.系数为一般模糊数的多元线性回归模型[J].统计与决策,2015,(3).
[6]Carlsson C,Fullér R.On Possibilistic Mean Valueand Variance of Fuzzy Numbers[J].Fuzzy Sets andSystems,2001,(122).
[7]Nasrabad M M.Narsabad E.A Mathematical-progrm-ming Approacg to Fuzzy Linear Regression Analysis[J].Applied Mathematics and Computation,2004,(155).
[8]Coppia R,Urso P D,Giordani P,et al.Least SquaresEstimation of a Linear Regression Model With LRFuzzy Response[J].Computational Statistics&DataAnalysis,2006,(51).
[9]黄华,易正俊.修正的模糊最小一乘线性回归[J].模糊系统与数学,2012,26(1).