ON QUASI NEWTON METHOD FOR SOLVING FUZZY NONLINEAR EQUATIONS

Umar A Omesa; Mustafa Mamat; Ibrahim M Sulaiman; Sukono Sukono

doi:10.46336/ijqrm.v1i1.1

ON QUASI NEWTON METHOD FOR SOLVING FUZZY NONLINEAR EQUATIONS

Umar A Omesa, Mustafa Mamat, Ibrahim M Sulaiman, Sukono Sukono

Abstract

This paper presents Quasi Newton’s (QN) approach for solving fuzzy nonlinear equations. The method considers an approximation of the Jacobian matrix which is updated as the iteration progresses. Numerical illustrations are carried, and the results shows that the proposed method is very encouraging.

Keywords

Quasi Newton’s method; Broyden’s method; fuzzy nonlinear equations; parametric form

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References

Abbasbandy, S and Asady, B. (2004) Newton's method for solving fuzzy nonlinear equations, Appl. Math. Comput, 156, 381-386.

Amirah, R. Lazim, M., and Mamat, M. (2010). Broyden’s method for solving Fuzzy nonlinear equations. Advances in fuzzy system, Article ID 763270, 6 pages.

Buckley, J. J. and Qu, Y. (1990) Solving linear and quadratic fuzzy equation. Fuzzy Set Syst. 38, 43-59.

Broyden, C. G. (1965). A class of methods for solving nonlinear simultaneous equations. Mathematics of computation, 19(92), 577-593.

Dennis, J, E. (1983). Numerical methods for unconstrained optimization and nonlinear equations. Prince-Hall, Inc., Englewood Cliffs, New Jersey, USA.

Dubois, D and Prade, H. (1980). Fuzzy Sets and Systems: Theory and Application, Academic Press, New York, USA.

Fang, J. (2002). On nonlinear equations for fuzzy mappings in probabilistic normed spaces. Fuzzy Sets and Systems, 131, 357-364.

Goetschel Jr, R. and Voxman, W. (1986). Elementary fuzzy calculus. Fuzzy set and Systems, 18, 31-43. Kajani, M. T., Asady, B., and Vencheh, A. H. (2005). An iterative method for solving dual fuzzy nonlinear equations. Applied Mathematics and Computation, 167, 316-323.

Kelley, C. T. (1995). Iterative Methods for Linear and Nonlinear Equations”. SIAM, Philadelphia, PA. Mamat, M., Muhammad, K., and Waziri, M. Y. (2014) Trapezoidal Broyden’s method for solving systems of nonlinear equations. Applied Mathematical Sciences, 8, 251-60.

Peeva, K. (1992) Fuzzy linear systems. Fuzzy Sets Syst, 49, 339-355.

Sulaiman, I. M., Mamat, M., and Waziri, M. Y. (2018). Shamanskii method for Solving Fuzzy Nonlinear Equation. Proc. of the 2nd IEEE Intl Conf on Intl Syst Engr (ICISE), Malaysia. pp. 20-21.

Sulaiman, I. M., Mamat, M., Mohamed, M. A., and Waziri, M. Y. (2018). Diagonal Updating Shamasnkii-Like method for Solving Fuzzy Nonlinear Equation. Far East Journal of Math Sci, 103(10), 1619-1629.

Sulaiman, I. M., Mamat, M., Waziri, M. Y., Mohamed, M. A., and Mohamad, F. S. (2018). Solving Fuzzy Nonlinear Equation via Levenberg-Marquardt Method. Far East Journal of Math Sci, 103(10), 1547-1558.

Sulaiman, I. M., Waziri, M. Y., Olowo, E. S., and Talat, A. N. (2018) Solving Fuzzy Nonlinear Equations with a New Class of Conjugate Gradient Method. Malaysian Journal of Computing and Applied Mathematics, 1(1), 11-19.

Waziri. M. Y. and Majid, Z. A. (2012). A new approach for solving dual Fuzzy nonlinear equations. Advances in Fuzzy Systems. Article ID 682087, 5 pages doi:10.1155/2012/682087 no. 25, 1205 - 1217. Waziri, M. Y. and Moyi, A. U. (2016). An alternative approach for solving dual fuzzy nonlinear equations. International Journal of Fuzzy Systems, 18(1), 103-107.

Zadeh, L. A. (1965) fuzzy sets. Information and Control, 8, 338-353.

DOI: https://doi.org/10.46336/ijqrm.v1i1.1