A neuro-fuzzy approach to compute the solution of a $Z$-numbers system with Trapezoidal fuzzy data

Document Type : Research Article

Authors

1 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

Linear systems of equations with $Z$-numbers have recently attracted some interest. Some approaches have been developed for solving these systems. Since, there are many ambiguities and uncertainties in such issues, there is no analytic solution for these kinds of systems. Therefore, numerical schemes are usually used to estimate the solution of them.  In this research, a computational scheme for solving linear systems involving trapezoidal $Z$-numbers is presented. The proposed approach is designed in such a way that it is firstly converted the $Z$-numbers coefficients to the corresponding fuzzy numbers and then using a ranking function, the fuzzy coefficients are converted to real coefficients. In this trend, after two stages, firstly, the original $Z$-numbers system becomes a fuzzy linear system and the fuzzy system is converted to a real system. Then, the obtained crisp linear system is solved based on the artificial neural network algorithm. Finally, two sample trapezoidal $Z$-numbers systems are solved based on the given approach to illustrate the process of the proposed algorithm.

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Journal of Mathematical Modeling
Volume 12, Issue 4
December 2024
Pages 753-767

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