An enhanced fuzzy linear regression model with more flexible spreads

One of the deficiencies of previous fuzzy linear regression models is that with the increase of the magnitudes of independent variables, the spreads of estimated fuzzy dependent variables are increasing, even though the spreads of observed dependent variables actually decrease or remain unchanged. Some solutions have been proposed to solve this spreads increasing problem. However, those solutions still cannot model a decreasing trend in the spreads of the observed dependent variables as the magnitudes of the independent variables increase. In this paper we propose an enhanced fuzzy linear regression model (model FLR"F"S), in which the spreads of the estimated dependent variables are able to fit the spreads of the observed dependent variables, no matter the spreads of the observed dependent variables are increased, decreased or unchanged as the magnitudes and spreads of the independent variables change. Four numerical examples are used to demonstrate the effectiveness of model FLR"F"S.

[1]  Ebrahim Nasrabadi,et al.  Fuzzy linear regression models with least square errors , 2005, Appl. Math. Comput..

[2]  C. R. Bector,et al.  A simple method for computation of fuzzy linear regression , 2005, Eur. J. Oper. Res..

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

[4]  Andrzej Bargiela,et al.  Multiple regression with fuzzy data , 2007, Fuzzy Sets Syst..

[5]  Lucien Duckstein,et al.  Multiobjective fuzzy regression with central tendency and possibilistic properties , 2002, Fuzzy Sets Syst..

[6]  Miin-Shen Yang,et al.  An omission approach for detecting outliers in fuzzy regression models , 2006, Fuzzy Sets Syst..

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

[8]  Chiang Kao,et al.  Entropy for fuzzy regression analysis , 2005, Int. J. Syst. Sci..

[9]  Shih-Pin Chen,et al.  A variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy , 2008, Inf. Sci..

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

[11]  Pierpaolo D'Urso,et al.  Regression analysis with fuzzy informational paradigm: a least-squares approach using membership function information , 2003 .

[12]  H. Shakouri,et al.  Fuzzy linear regression models with absolute errors and optimum uncertainty , 2007, 2007 IEEE International Conference on Industrial Engineering and Engineering Management.

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

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

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

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

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

[18]  J. Kacprzyk,et al.  Fuzzy regression analysis , 1992 .

[19]  Lucien Duckstein,et al.  Multi-objective fuzzy regression: a general framework , 2000, Comput. Oper. Res..

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

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

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

[23]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[24]  Cengiz Kahraman,et al.  Fuzzy Regression Approaches and Applications , 2006 .

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

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

[27]  Ebrahim Nasrabadi,et al.  Fuzzy linear regression analysis: a multi-objective programming approach , 2005, Appl. Math. Comput..

[28]  Renato Coppi,et al.  Management of uncertainty in Statistical Reasoning: The case of Regression Analysis , 2008, Int. J. Approx. Reason..

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