A new approach to solve fuzzy system of linear equations by Homotopy perturbation method
الموضوعات :M. Paripour 1 , J. Saeidian 2 , A. Sadeghi 3
1 - Department of Mathematics, Hamedan University of Technology, Hamedan, 65156-579, Iran
2 - Faculty of Mathematical Sciences and Computer, Kharazmi University,
50 Taleghani Avenue, Tehran 1561836314, Iran
3 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Arak, Iran
الکلمات المفتاحية: fuzzy number, Homotopy Perturbation method, Fuzzy system of linear equations, Auxiliary matrix,
ملخص المقالة :
In this paper, we present an efficient numerical algorithm for solving fuzzy systemsof linear equations based on homotopy perturbation method. The method is discussed indetail and illustrated by solving some numerical examples.
[1] S. Abbasbandy, R. Ezzati, Homotopy method for solving fuzzy nonlinear equations, Appl. Sci. 8 (2006), pp. 1-7.
[2] T. Allahviranloo, The Adomian decomposition method for fuzzy system of linear equations, Appl. Math. Comput. 163 (2) (2005), pp. 553-563.
[3] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Appl. Math. Comput. 155 (2) (2004), pp. 493-502.
[4] T. Allahviranloo, M. Ghanbari, Solving Fuzzy Linear Systems by Homotopy Perturbation Method, Inter. J. Comput. Cognition 8 (2) (2010), pp. 91-61.
[5] B. Asady, S. Abbasbandy, M. Alavi, Fuzzy general linear systems, Appl. Math. Comput. 169 (2005), pp. 34-40.
[6] E. Babolian, J. Saeidian, M. Paripour, Computing the Fourier Transform via Homotopy perturbation method, Z. Naturforsch. 64a (2009), pp. 671-675.
[7] D. Dubois, H. Prade, Fuzzy Set and Systems: Theory and Application, Academic Press, New York, 1980.
[8] M. Friedman, M. Ming, A. Kandel, Fuzzy linear systems, Fuzzy Sets Syst. 96 (1998), pp. 201-209.
[9] R. Goetschell, W. Voxman, Elementary calculus, Fuzzy Sets Syst. 18 (1986), pp. 31-43.
[10] J. H. He, Homotopy perturbation technique, Comp. Meth. Appl. Mech. Eng. 178 (1999), pp. 257-262.
[11] J. H. He, A coupling method of homotopy technique and a perturbation technique for non-linear problems, Int. J. Non-Linear Mech. 35 (1) (2000), pp. 37-43.
[12] J. H. He, Homotopy perturbation method: a new non-linear analytical technique, Appl. Math. Comput. 135 (1) (2003), pp. 73-79.
[13] B. Keramati, An approach to the solution of linear system of equations by He; homotopy perturbation method, Chaos, Solitons and Fractals. 37 (2006), pp. 1528-1537.
[14] H. Ku Liu, Application of homotopy perturbation methods for solving systems on linear equations, Appl. Math. Comput. 217 (2011), pp. 5259-5264.
[15] S. J. Liao, Beyond perturbation: An introduction to homotopy analysis method, Chapman Hall/CRC Press, Boca Raton, 2003.
[16] M. Ma, M. Friedman, A. Kandel, A new fuzzy arithmetic, Fuzzy Sets and Syst. 108 (1999), pp. 83-90.
[17] H. Saberi Naja, S. A. Edalatpanah, A. H. Refahi Sheikhani, Application of Homotopy Perturbation Method for Fuzzy Linear Systems and Comparison with Adomians Decomposition Method, Chinese Journal of Mathematics 2013 (2013), pp. 1-7.
[18] K. Wang, B. Zheng, Inconsistent fuzzy linear systems, Appl. Math. Comput. 181 (2006), pp. 973-981.
[19] B. Zheng, K. Wang, General fuzzy linear systems, Appl. Math. Comput. 181 (2006), pp. 1276-1286.