Weighted fuzzy ridge regression analysis with crisp inputs and triangular fuzzy outputs

In this paper a new weighted fuzzy ridge regression method for a given set of crisp input and asymmetrical triangular fuzzy output values is proposed. In this approach the non-linear regression function is obtained by mapping the input samples into a higher dimensional feature space via a kernel function and constructing a linear regression estimation function in it. The method has the advantage that the solution is obtained by solving a system of linear equations. For the illustration of the proposed method a number of examples of importance are considered and the results obtained are compared with that of other methods. The results clearly demonstrate the effectiveness of our proposed method.

[1]  Chiang Kao,et al.  A fuzzy linear regression model with better explanatory power , 2002, Fuzzy Sets Syst..

[2]  Phil Diamond,et al.  Fuzzy least squares , 1988, Inf. Sci..

[3]  Alexander Gammerman,et al.  Ridge Regression Learning Algorithm in Dual Variables , 1998, ICML.

[4]  Yun-Hsi O. Chang.  Hybrid fuzzy least-squares regression analysis and its reliability measures , 2001, Fuzzy Sets Syst..

[5]  Dug Hun Hong,et al.  Ridge estimation for regression models with crisp inputs and Gaussian fuzzy output , 2004, Fuzzy Sets Syst..

[6]  Pierpaolo D'Urso,et al.  Least squares estimation of a linear regression model with LR fuzzy response , 2006, Comput. Stat. Data Anal..

[7]  William H. Woodall,et al.  Properties of certain fuzzy linear regression methods , 1994 .

[8]  Ping-Teng Chang,et al.  A generalized fuzzy weighted least-squares regression , 1996, Fuzzy Sets Syst..

[9]  Hsien-Chung Wu,et al.  Fuzzy estimates of regression parameters in linear regression models for imprecise input and output data , 2003, Comput. Stat. Data Anal..

[10]  H. Moskowitz,et al.  Fuzzy versus statistical linear regression , 1996 .

[11]  Wolfgang Näther,et al.  Linear Regression with Random Fuzzy Variables: Extended Classical Estimates, Best Linear Estimates, Least Squares Estimates , 1998, Inf. Sci..

[12]  Yuh-Jye Lee,et al.  RSVM: Reduced Support Vector Machines , 2001, SDM.

[13]  Ebrahim Nasrabadi,et al.  A mathematical-programming approach to fuzzy linear regression analysis , 2004, Appl. Math. Comput..

[14]  Bilal M. Ayyub,et al.  Fuzzy regression methods - a comparative assessment , 2001, Fuzzy Sets Syst..

[15]  Hideo Tanaka,et al.  Fuzzy regression analysis using neural networks , 1992 .

[16]  E. Stanley Lee,et al.  Fuzzy regression with radial basis function network , 2001, Fuzzy Sets Syst..

[17]  Wenyi Zeng,et al.  Fuzzy Linear Regression Model , 2008, 2008 International Symposium on Information Science and Engineering.

[18]  Ning Wang,et al.  Fuzzy nonparametric regression based on local linear smoothing technique , 2007, Inf. Sci..

[19]  Glenn Fung,et al.  Proximal support vector machine classifiers , 2001, KDD '01.

[20]  Pierpaolo D'Urso,et al.  An "orderwise" polynomial regression procedure for fuzzy data , 2002, Fuzzy Sets Syst..