Research and Innovation Articles
Published 2010-09-21
Keywords
- Systems of fuzzy nonlinear equations,
- parametric form,
- Newton’s method
How to Cite
Cumsille, P., Ramírez Molina, J., & Rojas Medar, M. A. (2010). Numerical study of systems of fuzzy nonlinear equations. Revista Integración, Temas De matemáticas, 28(2), 153–172. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2173
Abstract
In this work we study the numerical resolution of systems of fuzzy nonlinear equations. More precisely, we describe, analyze and simulate numerical methods, such as Newton method, in order to approximate efficiently the solutions to such problems. One of the main issues of this type of problems is that the standard analytical techniques for finding solutions, are not appropriate to resolve them. For this reason, in this paper we focus in the study of known results for the classical methods and their adaptation to the resolution of fuzzy problems.
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References
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[2] Abbasbandy S. and Ezzati R., “Newton’s method for solving a system of fuzzy nonlinear equations”, Appl. Math. Comput., 175 (2006), 1189–1199.
[3] Abbasbandy S. and Jafarian A., “Steepest descent method for solving fuzzy nonlinear equations”, Appl. Math. Comput., 174 (2006), 669–675.
[4] Abbasbandy S. and Jafarian A., “Steepest descent method for system of fuzzy linear equations”, Appl. Math. Comput., 175 (2006), 823–833.
[5] Abbasbandy S., Nieto J.J., Ezzati R. and Rodríguez-López R., “Newton’s method for solving quadratic fuzzy equations”, Adv. Theor. Appl. Math., 1 (2006), 1–8.
[6] Argyros I.K., Convergence and applications of Newton-type iterations, Springer, New York, 2010.
[7] Asady B., Abbasbandy S. and Alavi M., “Fuzzy general linear systems”, Appl. Math. Comput., 169 (2005), 34–40.
[8] Buckley J.J., Eslami E. and Feuring T., “Fuzzy mathematics in economics and engineering”, vol. 91 of Studies in Fuzziness and Soft Computing, Physica-Verlag, Heidelberg, 2002.
[9] Buckley J.J. and Qu Y., “Solving linear and quadratic fuzzy equations”, Fuzzy Sets and Systems, 38 (1990), 43–59.
[10] Buckley J.J. and Qu Y., “Solving systems of linear fuzzy equations”, Fuzzy Sets and Systems, 43 (1991), 33–43.