ESTIMATING THE PARAMETERS OF A FUZZY LINEAR REGRESSION MODEL

Document Type: Research Paper

Authors

1 Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran

2 Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

Fuzzy linear regression models are used to obtain an appropriate
linear relation between a dependent variable and several independent variables
in a fuzzy environment. Several methods for evaluating fuzzy coefficients in
linear regression models have been proposed. The first attempts at estimating
the parameters of a fuzzy regression model used mathematical programming
methods. In this thesis, we generalize the metric defined by Diamond and
use it as a criterion to estimate these parameters. Our method, is not only
computationally easy to handle, but, when compared with earlier methods,
has a smaller the sum of errors of estimation.

Keywords


[1] P. Diamond,Fuzzy least squares, Information Sciences, 46 (1988), 141-157.

[2] D. H. Hong and C. Hwang,Support vector fuzzy regression machines, Fuzzy Sets and Systems,

138(2003), 271-281.

[3] C. Kao and C. Chyu,A fuzzy linear regression model with better explanatory power, Fuzzy

Sets and Systems,126 (2002), 401-409.

[4] C. Kao and C. Chyu,Least-squares estimates in fuzzy regression analysis, European J. Oper.

Res.,148 (2003), 426-435.

[5] N. Kim , R. R. Bishu,Evaluation of fuzzy linear regression models by comparing membership

functions, Fuzzy Sets and Systems, 100 (1998), 343-353.

[6] M. L. Puri and D. A. Ralescu,Fuzzy random variables, J. Math. Anal. Appl., 114 (1986),

409-422.

[7] M. Sakawa and H. Yano,Multiobjective fuzzy linear regression analysis for fuzzy input-output

data, Fuzzy Sets and Systems, 47 (1992), 173-181.

 

[8] H. Tanaka,Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems,

24(1987), 363-375.

[9] H. Tanaka, I. Hayashi and J.Watada,Possibilistic linear regression analysis with fuzzy model,

European J. Oper. Res.,40 (1989), 389-396.

[10] H. Tanaka and H. Lee,Interval regression analysis by quadratic programming approach, IEEE

Trans. Systems Man Cybrnet.,6(4)(1988), 473-481.

[11] H. Tanaka , S. Uegima and K. Asai,Linear regression analysis with fuzzy model. IEEE Trans.

Systems Man Cybrnet.,12(6)(1982), 903-907.

[12] H. Tanaka and J. Watada,Possibilistic systems and their application to the linear regression

model, Fuzzy Sets and Systems, 27(1988), 275-289.

[13] M. Yang and T. Lin,Fuzzy least-squares linear regression analysis for fuzzy input-output

data, Fuzzy Sets and Systems, 126 (2002), 389-399.