Fuzzy nonparametric regression based on local linear smoothing technique

In a great deal of literature on fuzzy regression analysis, most of research has focused on some predefined parametric forms of fuzzy regression relationships, especially on the fuzzy linear regression models. In many practical situations, it may be unrealistic to predetermine a fuzzy parametric regression relationship. In this paper, a fuzzy nonparametric model with crisp input and LR fuzzy output is considered and, based on the distance measure for fuzzy numbers suggested by Diamond [P. Diamond, Fuzzy least squares, Information Sciences 46 (1988) 141-157], the local linear smoothing technique in statistics with the cross-validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit this model. Some simulation experiments are conducted to examine the performance of the proposed method and three real-world datasets are analyzed to illustrate the application of the proposed method. The results demonstrate that the proposed method works quite well not only in producing satisfactory estimate of the fuzzy regression function, but also in reducing the boundary effect significantly.

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

[2]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[3]  H. Ishibuchi,et al.  An architecture of neural networks with interval weights and its application to fuzzy regression analysis , 1993 .

[4]  Carlo Bertoluzza,et al.  On a new class of distances between fuzzy numbers , 1995 .

[5]  Berlin Wu,et al.  A new approach to fuzzy regression models with application to business cycle analysis , 2002, Fuzzy Sets Syst..

[6]  Hong Tau Lee,et al.  Fuzzy regression model with fuzzy input and output data for manpower forecasting , 2001, Fuzzy Sets Syst..

[7]  Dug Hun Hong,et al.  Support vector fuzzy regression machines , 2003, Fuzzy Sets Syst..

[8]  E. Lee,et al.  Nonparametric fuzzy regression—k-NN and kernel smoothing techniques , 1999 .

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

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

[11]  Miin-Shen Yang,et al.  Fuzzy least-squares linear regression analysis for fuzzy input-output data , 2002, Fuzzy Sets Syst..

[12]  Hideo Tanaka,et al.  FUZZY APPROXIMATIONS WITH NON-SYMMETRIC FUZZY PARAMETERS IN FUZZY REGRESSION ANALYSIS , 1999 .

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

[14]  Sandra A. Santos,et al.  Parallel projection methods and the resolution of ill-posed problems , 1994 .

[15]  E. Lee,et al.  Ranking of fuzzy sets based on the concept of existence , 1994 .

[16]  Miin-Shen Yang,et al.  Fuzzy least-squares algorithms for interactive fuzzy linear regression models , 2003, Fuzzy Sets Syst..

[17]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .

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

[19]  Ruoning Xu,et al.  Multidimensional least-squares fitting with a fuzzy model , 2001, Fuzzy Sets Syst..

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

[21]  Ram R. Bishu,et al.  Evaluation of fuzzy linear regression models by comparing membership functions , 1998, Fuzzy Sets Syst..

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

[23]  Dug Hun Hong,et al.  Extended fuzzy regression models using regularization method , 2004, Inf. Sci..

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

[25]  Wolfgang Härdle,et al.  Applied Nonparametric Regression , 1991 .

[26]  Jeffrey D. Hart,et al.  Nonparametric Smoothing and Lack-Of-Fit Tests , 1997 .

[27]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[28]  Pierpaolo D'Urso,et al.  A least-squares approach to fuzzy linear regression analysis , 2000 .

[29]  Hideo Tanaka,et al.  A Neural Network with Interval Weights and Its Application to Fuzzy Regression Analysis , 1992 .

[30]  Jorge de Andrés Sánchez,et al.  APPLICATIONS OF FUZZY REGRESSION IN ACTUARIAL ANALYSIS , 2003 .

[31]  Miin-Shen Yang,et al.  A fuzzy multiple linear regression based loss formula in electric distribution systems , 2004, Fuzzy Sets Syst..

[32]  Debjani Chakraborty,et al.  A Linear Regression Model in Fuzzy Environment Based on S-Curve , 2009 .

[33]  Dug Hun Hong,et al.  Fuzzy least-squares linear regression analysis using shape preserving operations , 2001, Inf. Sci..

[34]  Miin-Shen Yang,et al.  On a class of fuzzy c-numbers clustering procedures for fuzzy data , 1996, Fuzzy Sets Syst..

[35]  Pierpaolo D'Urso,et al.  Linear regression analysis for fuzzy = crisp input and fuzzy = crisp output data , 2015 .

[36]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

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