Estimating the parameters of fuzzy linear regression model with crisp inputs and Gaussian fuzzy outputs: A goal programm
- PDF / 609,277 Bytes
- 10 Pages / 595.276 x 790.866 pts Page_size
- 26 Downloads / 190 Views
METHODOLOGIES AND APPLICATION
Estimating the parameters of fuzzy linear regression model with crisp inputs and Gaussian fuzzy outputs: A goal programming approach E. Hosseinzadeh1 · H. Hassanpour2
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we offered a new method to fit a fuzzy linear regression model to a set of crisp inputs and Gaussian fuzzy outputs, by considering its parameters as Gaussian fuzzy numbers. To calculate the regression coefficients, a nonlinear programming model is formulated based on a new distance between Gaussian fuzzy numbers. The nonlinear programming model is converted to a goal programming model by choosing appropriate deviation variables and then to a linear programming which can be solved simply by simplex method. To show the efficiency of proposed model, some applicative examples are solved and three simulation studies are performed. The computational results are compared with some earlier methods. Keywords Goal programming · Fuzzy linear regression · Gaussian fuzzy number
1 Introduction Regression analysis is a powerful statistical methodology to analyze the phenomena in which one variable named output (response or dependent) variable depends on one or more variables named input (explanatory or independent) variables. Fuzzy linear regression (FLR) can be quite useful where available data are imprecise or uncertain. So there are many researches devoted to solve the problem. One approach to deal with FLR is linear programming (LP) approach, which was first introduced by Tanaka et al. (1982) and is based on minimizing fuzziness as an optimality criterion. Their method then was developed by others (e.g., see Hojati et al. 2005; Hung and Yang 2006; Özelkan and Duckstein 2000; Peters 1994; Sakawa and Yano 1992; Savic and Pedrycz 1991). Another approach is least-squares approach, which was first introduced by (Celmin, š 1987) and developed by others (see e.g. (Coppi et al. 2006; Kao and Chyu 2003; Modarres et al. 2005; Wunsche and Naether 2002; Yang and
Communicated by V. Loia.
B
E. Hosseinzadeh [email protected]
1
Department of mathematics, Kosar university of Bojnord, Bojnord, Iran
2
Department of Mathematics, University of Birjand, Birjand, Iran
Lin 2002)). This method used least-squares of residuals as a fitting criterion. (Xu 1991) proposed a distance on fuzzy numbers space by the integral of distances between all level sets. This distance can synthetically reflect the information on different membership degrees. Based on this distance, (Xu and Li 2001) discussed the problem of multidimensional least-squares fitting, and proposed a fuzzy linear regression model as an analogue of traditional linear least squares. (Özelkan and Duckstein 2000) developed several multi-objective fuzzy regression techniques to overcome some shortcoming of fuzzy regression by enabling the decision maker to select a non-dominated solution based on the tradeoff between data outliers and prediction vagueness. (Wu and Law 2010) proposed a new fuzzy support
Data Loading...
