模糊最小一乘线性回归  

FUZZY LEAST ABSOLUTE LINEAR REGRESSION

作　　者：冯启磊[1] 曾文艺[2] 

机构地区：[1]北京师范大学数学科学学院,北京100875 [2]北京师范大学信息科学与技术学院,北京100875

出　　处：《北京师范大学学报（自然科学版）》2008年第4期348-353,共6页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(60775032);教育部博士点基金资助项目(20020027013);教育部科学技术重点项目(03184);国家"九七三"计划资助项目(2002CB312200)

摘　　要：针对输入和输出的模糊数据,根据最小一乘准则,提出了基于对称三角模糊数的模糊最小一乘线性回归模型,并将它转化成线性规划问题,应用Matlab进行求解,通过实例,并与Tanaka,Diamond,Kim-Bishu,Kao-Chyu,Nasrabadi,Chang等模型相比较,验证了我们的模型具有更优的拟合性和良好的稳定性.Aiming at crisp input and fuzzy output, a certain distance between fuzzy numbers was introduced. Fuzzy least absolute linear regression model based on this distance was introduced and was transformed into linear programming; some theoretical conclusions and algorithm was investigated in detail. Finally, three numerical examples were used to illustrate that the proposed model was reasonable in comparison with Tanaka, Diamond, Kim-Bishu, Kao-Chyu, Nasrabadi and Chang models.

关 键 词：模糊数据 模糊最小一乘 模糊线性回归 参数估计 

分 类 号：O212.1[理学—概率论与数理统计] TP311.13[理学—数学]