| Title of paper:
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Derivative-free Newton's method for solving intuitionistic fuzzy nonlinear equations with an application
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| Author(s):
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| A. O. Umar
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| Department of Mathematics, Federal University of Agriculture, Zuru, Kebbi, Nigeria
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| umarabdul64@gmail.com
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| M. Y. Waziri
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| Department of Mathematics, Bayero University, Kano, Nigeria
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| mywaziri@gmail.com
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| A. U. Moyi
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| Department of Mathematics, Federal University, Gusau, Nigeria
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| aliyumoyik@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 2, pages 149–160
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| DOI:
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https://doi.org/10.7546/nifs.2022.28.2.149-160
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| Download:
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 PDF (550 Kb, File info)
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| Abstract:
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In this paper, we present a derivative-free Newton’s method that avoids computing the derivative by generating an approximation of the derivative for the intuitionistic fuzzy nonlinear equation. We first consider transforming the intuitionistic fuzzy quantities into their equivalent membership and non-membership parametric forms and insert the approximation from the forward difference method applied to [math]\displaystyle{ F'(x_k) = 0 }[/math] in Newton’s method to avoid computing the Jacobian matrix. Numerical experiments were carried out, which shows that the approach is a good option for computing Jacobian and is an efficient one.
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| Keywords:
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Derivative-free, Intuitionistic fuzzy nonlinear equation, Parametric form, Zadeh’s fuzzy set.
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| AMS Classification:
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03E72, 94-04.
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| References:
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