A mathematical-programming approach to fuzzy linear regression analysis

Most of previous studies on fuzzy regression analysis have a common characteristic of increasing spreads for the estimated fuzzy responses as the independent variable increases its magnitude, which is not suitable for general cases. In this paper, fuzzy linear regression models with fuzzy/crisp output, fuzzy/crisp input are considered, and an estimated method along with a mathematical-programming-based approach is proposed. The advantages of the proposed approach are simplicity in programming and computation, and minimum difference of total spread between observed and estimated values.

[1]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

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

[3]  Masatoshi Sakawa,et al.  Multiobjective fuzzy linear regression analysis for fuzzy input-output data , 1992 .

[4]  J. Watada,et al.  Possibilistic linear systems and their application to the linear regression model , 1988 .

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

[6]  Ping-Teng Chang,et al.  Applying fuzzy linear regression to VDT legibility , 1996, Fuzzy Sets Syst..

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

[8]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[9]  Witold Pedrycz,et al.  Evaluation of fuzzy linear regression models , 1991 .

[10]  Ruey-Chyn Tsaur,et al.  Fuzzy Regression for Seasonal Time Series Analysis , 2002, Int. J. Inf. Technol. Decis. Mak..

[11]  Dug Hun Hong,et al.  Fuzzy linear regression analysis for fuzzy input-output data using shape-preserving operations , 2001, Fuzzy Sets Syst..

[12]  Gwo-Hshiung Tzeng,et al.  A fuzzy seasonal ARIMA model for forecasting , 2002, Fuzzy Sets Syst..

[13]  H. Tanka.  Fuzzy data analysis by possibilistic linear models , 1987 .

[14]  Junzo Watada,et al.  Possibilistic linear regression analysis for fuzzy data , 1989 .

[15]  Hsiao-Fan Wang,et al.  Resolution of fuzzy regression model , 2000, Eur. J. Oper. Res..

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

[17]  Ping-Teng Chang,et al.  Fuzzy seasonality forecasting , 1997, Fuzzy Sets Syst..

[18]  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..

[19]  Chiang Kao,et al.  Least-squares estimates in fuzzy regression analysis , 2003, Eur. J. Oper. Res..

[20]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

[21]  A. Kandel,et al.  Fuzzy linear regression and its applications to forecasting in uncertain environment , 1985 .

[22]  Toly Chen,et al.  Forecasting methods using fuzzy concepts , 1999, Fuzzy Sets Syst..

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

[24]  Shing I. Chang,et al.  A fuzzy approach for multiresponse optimization: An off-line quality engineering problem , 1994 .

[25]  Hsiao-Fan Wang,et al.  Insight of a fuzzy regression model , 2000, Fuzzy Sets Syst..