基于正态模糊数回归分析模型的构建与评价被引量：7

下载PDF

导出

摘要文章采用模糊最小二乘法,求解自变量为精确数、因变量和回归系数均是正态模糊数的一元线性模糊回归模型,证明所求得的模糊估计量具有的统计性质:线性性与无偏性。给出模糊回归模型的残差、残差平方和及拟合优度公式。将方法应用于一个实际问题,并与经典回归分析进行比较,验证了该参数估计方法的合理性与有效性。

作者顾翠伶朱思峰

机构地区周口师范学院数学与统计学院

出处《统计与决策》 CSSCI 北大核心 2016年第13期21-25,共5页 Statistics & Decision

基金国家自然科学基金委-河南省人民政府人才培养联合基金项目(U1204618)

关键词正态模糊数模糊回归分析模糊最小二乘拟合程度

参考文献11

1Tanaka H, Uejima S, Asai K. Linear Regression Analysis with Fuzzy Model[J]. IEEE Trans. Systems, Man Cyber, 1982,(12).
2Diamond P. Fuzzy Least Squares[J].Information Science, 1988,(46).
3Chang Y H, Ayyub B M. Fuzzy Regression Methods---A Compara- tive Assessment[J]. Fuzzy Sets and Systems, 2011, 119(2).
4Chang Y H. Hybrid Fuzzy Least-squares Regression Analysis and its Reliability Measures[J]. Fuzzy Sets and Systems, 2011.
5Sakawa M, "Yano H. Multiobjective Fuzzy Liear Regression Analysis for Fuzzy Input-out Data[J]. Fuzzy Set and Systems, 1992.
6张爱武.系数为LR型模糊数的模糊回归模型的参数估计[J].模糊系统与数学,2013,27(6):140-147. 被引量：3
7张爱武.系数为梯形模糊数的模糊回归分析的最小二乘法[J].数学的实践与认识,2012,42(22):235-244. 被引量：4
8Parvathi R, Malathi C, Akram M, et al. Intuitionistic Fuzzy Linear Regression Analysis[J].Fuzzy Optimization and Decision Making, 2013.
9彭祖赠,孙韫玉.模糊数学及其应用[M].武汉:武汉大学出版社,2007.
10李安责,张志宏,孟艳等.模糊数学及其应用(第二版)[M].北京:冶金工业出版社.2005.

1梁艳,魏立力.系数为LR-型模糊数的模糊线性最小二乘回归[J].模糊系统与数学,2007,21(3):111-117. 被引量：8
2Thanaka H, Uejina S and Asai K. Fuzzy linear regression model[J]. IEEE Trans Systems Man Cybernetics, 1980(10): 2933-2938.
3Thanaka H, Uejina S and Asai K. Linear regression analysis with fuzzy model[J]. IEEE Trans Systems Man Cybernetics, 1982(12): 903-907.
4Thanaka H. F~zzy data analysis by possibilistic linear model[J]. Fuzzy Sets and Systems, 1987(24): 363-375.
5Thanaka H, Watada J. Possibilistic linear systems and their application to the linear regression model[J]. Fuzzy Sets and Systems, 1988(27): 145-160.
6Diamond P. Fuzzy least squares[J]. Information Science, 1988(46): 141-157.
7Chang Y H O, Ayyub B M. Fuzzy regression methods-a comparetive assessment[J]. Fuzzy Sets and Systems, 2001(119): 187-203.
8Xu R N, Li C L. Multidimensional least squares fitting with a fuzzy model[J]. Fuzzy Sets and Systems, 2001(119): 215-223.
9Cope R, D'Urso P,Giordani P and Santoro A. Least squares estimation of a linear regression model with LR fuzzy response[J]. Computational Statististics ~ Data Analysis, 2006(51): 267-286.
10Ban A. Approximattion of fuzzy numbers by trapeziondal fuzzy numbers preseving the expected interval[J]. Fuzzy Sets and Systems, 2008(159): 1327-1344.