Numerical solution of a system of fuzzy polynomial equations by modified Adomian decomposition method

Subject Areas : History and biography

M. Mosleh ¹ (Department of Mathematics, Islamic Azad University, Firoozkooh Branch, Firoozkooh, Iran)

Received: 2016-05-10 Accepted : 2017-11-01 Published : 2017-12-01

Keywords: fuzzy numbers, Adomian decomposition method, system of polynomials,

Abstract :

In this paper, we present some efficient numericalalgorithm for solving system of fuzzy polynomial equations based on Newton'smethod. The modified Adomian decomposition method is applied toconstruct the numerical algorithms. Some numerical illustrationsare given to show the efficiency of algorithms.

References:

[1] K. Abbaoui, Y. Cherruault, V. Seng, Practical formulae for the calculuse of multivariable Adomian polynomials, Comput. Model. 22 (1995), 89-93.

[2] K. Abbaoui, Y. Cherruault, Convergence of Adomian’s method applied to nonlinear equations, Math. Com- put. Model. 20 (9) (1994), 69-73.

[3] S. Abbasbandy, Improving Newton- Raphson method for nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 145 (2003), 887-893.

[4] S. Abbasbandy, Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 170 (2005), 648-656.

[5] S. Abbasbandy, B. Asady, Newtons method for solving fuzzy nonlinear equations, Appl. Math. Comput. 159 (2004), 349-356.

[6] S. Abbasbandy, R. Ezzati, Newton’s method for solving a system of fuzzy nonlinear equations, Appl. Math. Comput. 175 (2006) 1189-1199.

[7] S. Abbasbandy, A. Jafarian, Steepest descent method for solving fuzzy nonlinear equations, Appl. Math. Comput. 175 (2006) 823-833.

[8] S. Abbasbandy, M. Otadi, Numerical solution of fuzzy polynomials by fuzzy neural network, Appl. Math.Comput. 181 (2006), 1084-1089.

[9] S. Abbasbandy, M. Otadi, M. Mosleh, Numerical solution of a system of fuzzy polynomials by fuzzy neural network, Inform. Sci. 178 (2008), 1948-1960.

[10] G. Adomian, Nonlinear stochastic system and approximations to physics, klower academic publisher, Dordrecht, 1989.

[11] G. Adomian, R. Rach, On the solution of algebraic equations by yhe decomposition method, Math. Anal. Appl. 105 (1985), 141-166.

[12] T. Allahviranloo, M. Otadi, M. Mosleh, Iterative method for fuzzy equations, Soft Comput. 12 (2007), 935- 939.

[13] S. S. L. Cheng, L. A. Zadeh, On fuzzy mapping and conterol, IEEE Transactions on Systems, Man and Cybernetics. 2 (1972), 30-34.

[14] Y. J. Cho, N. J. Huang, S. M. Kang, Nonlinear equations for fuzzy mapping in probabilistic normed spaces, Fuzzy Sets Syst. 110 (2000), 115-122.

[15] D. Dubois, H. Prade, Operations on fuzzy numbers, Journal of Systems Science. 9 (1978), 613-626.

[16] D. Dubois, H. Prade, Fuzzy Sets and Systms: Theory and Application, Academic Press, New York, 1980.

[17] J. Fang, On nonlinear equations for fuzzy mapping in probabilistic normed spaces, Fuzzy Sets Syst. 131 (2002), 357-364.

[18] R. Goetschel, W. Voxman, Elementary calculus, Fuzzy Sets Syst. 18 (1986), 31-43.

[19] J. Ma, G. Feng, An approach to H∞ control of fuzzy dynamic systems, Fuzzy Sets Syst. 137 (2003), 367-386.

[20] S. Nahmias, Fuzzy variables, Fuzzy Sets and Systems. 12 (1978), 97-111.

[21] J. J. Nieto, R. Rodriguez-Lopez, Existence of extremal solutions for quadratic fuzzy equations. Fixed Point Theory and Appl. 3 (2005), 321-342.

[22] M. Otadi, M. Mosleh, Solution of fuzzy polynomial equations by modified Adomian decomposition method, Soft Computing, In press.

[23] M. Tavassoli Kajani, B. Asady, A. Hadi Vencheh, An iterative method for solving dual fuzzy nonlinear equations. Appl. Math. Comput. 167 (2005), 316-323.

[24] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353.

[25] H. J. Zimmermann, Fuzzy Sets Theory and its Application, Kluwer Academic Press, Dordrecht, 1991.