A matrix method for estimating linear regression coefficients based on fuzzy numbers

Subject Areas : Statistics

S. Ezadi ¹ , T. allahviranllo ^{2 *}

1 - Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65138, Iran.
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778, Iran.

Received: 2018-09-18 Accepted : 2018-10-14 Published : 2019-02-20

Keywords: اعداد- زاده, رگرسیون خطی مبتنی بر اعداد-زاد, روش ماتریسی,

Abstract :

In this paper, a new method for estimating the linear regression coefficients approximation is presented based on Z-numbers. In this model, observations are real numbers, regression coefficients and dependent variables (y) have values ​​for Z-numbers. To estimate the coefficients of this model, we first convert the linear regression model based on Z-numbers into two fuzzy linear regression models, and then convert the two models into Ax = y, in which A is the linear regression coefficient and x is the independent variable and y variable It Depends, where A is the linear regression coefficient and x is independent variable and y is dependent variable. Finally, to minimize this device, we use the total sum of squared error based on distance d. In two examples, the proposed method is compared with the only available method.

References:

[1] C.B. Cheng, E.S. Lee, Fuzzy regression with radial basis function network, Fuzzy Sets and Systems 119 (2) (2001) 291–301.

[2] A. Bardossy, Note on fuzzy regression, Fuzzy Sets and Systems 37 (1990) 65–75.

 

[3] A. Bardossy, I. Bogardi, L. Duckstein, Fuzzy regression in hydrology,Water Resources Res. 26 (1990) 1497–1508.

 

[4] L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965) 338–353.

 

[5] L.A. Zadeh, Fuzzy sets and information granularity, in: M.M. Gupta, R.K. Ragade, R.R. Yager (Eds.), Advances in Fuzzy Set Theory and Applications, North Holland, Amsterdam, (1979), pp. 3–18.

 

[6] L.A. Zadeh, Fuzzy logic = computing with words, IEEE Trans. Fuzzy Systems 4 (2) (1996) 103–111.

[7] H. Tanaka, Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems, 24(1987), 363-375.

 

 [8] H. Tanaka, I. Havashi and J. Watada,. Possibilistic Liner regression analysis for fuzzy data, European J. Oper. Res., (1989)   40: 389-396.

 

 [9] J. Mohammadi, S. M. Taheri, Pedomodels  fitting with fuzzy least squares regression, Iraninan J. Fuzzy Systems, (2004) 1 (2): 45-61.

 

[10] R. Xu, C. Li, Multidimentional least-squares fitting with a fuzzy model, fuzzy Sets and Systems, (2001)119: 215-223.

 

 [11] M. Hojati, C. R. Bector, Smimou K. A Simple Method of Fuzzy Linear Regression. European Journal of Operational Research (2005); 166; 172-184.

 

[12] G. Peters, Fuzy Linear Regression with fuzzy intervals. Fuzzy Sets and Systems (1994); 63; 45-55.

 

[13] L.A. Zadeh, A Note on Z-numbers, Information Sciences 181 (2011) 2923–2932.

[14] S. Ezadi, T.  Allahviranloo, Numerical solution of linear regression based on Z-numbers by improved neural network, paper accept.

 

[15] S. Ezadi, T. Allahviranloo, New multi-layer method for Z-number ranking using Hyperbolic Tangent function and convex combination, Intelligent Automation Soft Computing., (2017), 1-7.

 

[16] S. Ezadi, T. Allahviranloo, Two new methods for ranking of Z-numbers based on sigmoid function and sign method, International Journal of Intelligent Systems., (2018), 1-12.

 

[17] B. Kang, D. WEI, Y. LI and Y. DENG, Decision Making Using Z-numbers under Uncertain Environment, Journal of Computational Information Systems, 7 (2012) 2807–2814.

 

 [18] B. Kang, D. Wei, Y. Li, Y. Deng, A method of converting Z-number to classical fuzzy number, Journal of Information and Computational Scienc., 3 ( 2012), 703-709.

 

[19] R.A. Alive, A.V. Alizadeh, O.H. Huseynov, The arithmetic of discrete Z-numbers, Inform. Sciences., 290 (2015) 134-155.

 

[20] R.A. Alive, O.H. Huseynov, R.R. Alive, A.V. Alizadeh, The arithmetic of Z-numbers. Theory and Applications, World Scientific, Singapore, (2015).

 

[21] R.A. Alive, O.H. Huseynov, and R. Serdaroglu, Ranking of Z-numbers, and its Application in Decision Making. Int. J.

 

[22] ASA. Bakar, A. Gegov, (2015) Multi-layer decision methodology for ranking Z-numbers. Int J Comput Intell Syst, 8:395–406.

 

[23] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic, Boston, (1991).