Abstract
In this paper, we present some efficient numerical algorithm for solving fuzzy polynomial equations based on Newton’s method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms.
Similar content being viewed by others
References
Abbaoui K, Cherruault Y (1994) Convergence of Adomian’s method applied to nonlinear equations. Math Comput Model 20(9):69–73
Abbaoui K, Cherruault Y, Seng V (1995) Practical formulae for the calculuse of multivariable Adomian polynomials. Comput Model 22:89–93
Abbasbandy S (2003) Improving Newton–Raphson method for nonlinear equations by modified Adomian decomposition method. Appl Math Comput 145:887–893
Abbasbandy S (2005) Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method. Appl Math Comput 170:648–656
Abbasbandy S, Asady B (2004) Newtons method for solving fuzzy nonlinear equations. Appl Math Comput 159:349–356
Abbasbandy S, Ezzati R (2006) Newton’s method for solving a system of fuzzy nonlinear equations. Appl Math Comput 175:1189–1199
Abbasbandy S, Jafarian A (2006) Steepest descent method for solving fuzzy nonlinear equations. Appl Math Comput 175:823–833
Abbasbandy S, Otadi M (2006) Numerical solution of fuzzy polynomials by fuzzy neural network. Appl Math Comput 181:1084–1089
Abbasbandy S, Otadi M, Mosleh M (2008) Numerical solution of a system of fuzzy polynomials by fuzzy neural network. Inf Sci 178:1948–1960
Adomian G (1989) Nonlinear stochastic system and approximations to physics. Kluwer, Dordrecht
Adomian G, Rach R (1985) On the solution of algebraic equations by yhe decomposition method. Math Anal Appl 105:141–166
Allahviranloo T, Otadi M, Mosleh M (2007) Iterative method for fuzzy equations. Soft Comput 12:935–939
Buckley JJ, Qu Y (1991) Solving fuzzy equations: a new solutions concept. Fuzzy Sets Syst 39:291–301
Cheng SSL, Zadeh LA (1972) On fuzzy mapping and control. IEEE Trans Sys Man Cybernet 2:30–34
Cho YJ, Huang NJ, Kang SM (2000) Nonlinear equations for fuzzy mapping in probabilistic normed spaces. Fuzzy Sets Syst 110:115–122
Dubois D, Prade H (1978) Operations on fuzzy numbers. J Syst Sci 9:613–626
Dubois D, Prade H (1980) Fuzzy sets and systems: theory and application. Academic Press, New York
Fang J (2002) On nonlinear equations for fuzzy mapping in probabilistic normed spaces. Fuzzy Sets Syst 131:357–364
Goetschel R, Voxman W (1986) Elementary calculus. Fuzzy Sets Syst 18:31–43
Kajani MT, Asady B, Vencheh AH (2005) An iterative method for solving dual fuzzy nonlinear equations. Appl Math Comput 167:316–323
Ma J, Feng G (2003) An approach to H ∞ control of fuzzy dynamic systems. Fuzzy Sets Syst 137:367–386
Nahmias S (1978) Fuzzy variables. Fuzzy Sets Syst 12:97–111
Nieto JJ, Rodriguez-Lopez R (2005) Existence of extremal solutions for quadratic fuzzy equations. Fixed Point Theory Appl 3:321–342
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zimmermann HJ (1991) Fuzzy sets theory and its application. Kluwer, Dordrecht
Acknowledgments
We would like to thank Professor S. Abbasbandy and the referees for valuable suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Otadi, M., Mosleh, M. Solution of fuzzy polynomial equations by modified Adomian decomposition method. Soft Comput 15, 187–192 (2011). https://doi.org/10.1007/s00500-010-0546-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-010-0546-6