Shamanskii method for solving parameterized fuzzy nonlinear equations

Authors

DOI:

https://doi.org/10.11121/ijocta.01.2021.00843

Keywords:

Shamanskii method, Fuzzy nonlinear equations, Parameterized fuzzy equations, Numerical experiments

Abstract

One of the most significant problems in fuzzy set theory is solving fuzzy nonlinear equations. Numerous researches have been done on numerical methods for solving these problems, but numerical investigation indicates that most of the methods are computationally expensive due to computing and storage of Jacobian or approximate Jacobian at every iteration. This paper presents the Shamanskii algorithm, a variant of Newton method for solving nonlinear equation with fuzzy variables. The algorithm begins with Newton’s step at first iteration, followed by several Chord steps thereby reducing the high cost of Jacobian or approximate Jacobian evaluation during the iteration process. The fuzzy coe?cients of the nonlinear systems are parameterized before applying the proposed algorithm to obtain their solutions. Preliminary results of some benchmark problems and comparisons with existing methods show that the proposed method is promising.

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Author Biographies

Sulaiman Mohammed Ibrahim, Universiti Sultan Zainal Abidin, Gong Badak Campus, Kuala Terengganu, 21300, Malaysia

Ibrahim Sulaiman Mohammed is currently a post-doctoral researcher at Faculty of informatics and computing, Universiti Sultan Zainal Abidin (UniSZA), Malaysia from 2019 till date. He obtained his PhD from UniSZA in 2018 specializing in the field of fuzzy systems. His research interest includes Numerical research, Fuzzy nonlinear systems, unconstrained optimization.

Mustafa Mamat, Universiti Sultan Zainal Abidin, Malaysia

Mustafa Mamat is currently a Professor of Computational and Applied Mathematics at Universiti Sultan Zainal Abidin (UniSZA), Malaysia since 2013. He obtained his PhD from UMT in 2007 specialization in optimization field. To date, he has successfully supervised more than 70 postgraduate students and published more than 260 research papers in various international journals and conferences. His research interest includes unconstrained optimization such as conjugate gradient methods and chaotic systems. Currently, he is the Editor in Chief for Malaysian Journal of Computing and Applied Mathematics (a UniSZA journal in applied science) and an editor for Indonesian Journal of Science and Technology.

Puspa Liza Ghazali, Universiti Sultan Zainal Abidin, Kuala Terengganu, Malaysia

Puspa Liza Ghazali is currently an Associate Professor of Business and Management at Universiti Sultan Zainal Abidin (UniSZA), Malaysia since 2018. She obtained her PhD from Universiti Malaysia Terengganu (UMT) in 2013 specialization in Financial Mathematics. Her research interest includes Financial Mathematics, Islamic Insurance, Insurance, Mathematical Science, Statistical Modelling and optimization.  Currently, she is the one of the Editorial Board in Journal of Management Theory and Practice (a UniSZA journal in Management).

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Published

2020-12-10
CITATION
DOI: 10.11121/ijocta.01.2021.00843
Published: 2020-12-10

How to Cite

Ibrahim, S. M., Mamat, M., & Ghazali, P. L. . (2020). Shamanskii method for solving parameterized fuzzy nonlinear equations. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(1), 24–29. https://doi.org/10.11121/ijocta.01.2021.00843

Issue

Vol. 11 No. 1 (2021): IJOCTA

Section

Research Articles

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Copyright (c) 2020 Sulaiman Mohammed Ibrahim

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