A novel hybridized neuro-fuzzy model for solving fuzzy singular perturbation problems with initial conditions

Al-Abrahemee, Khalid Mindeel Mohammed

doi:10.47974/JIM-1627

Open Access Research Article

A novel hybridized neuro-fuzzy model for solving fuzzy singular perturbation problems with initial conditions

^*Khalid Mindeel Mohammed Al-AbrahemeeCorresponding authorKhalid.mohammed@qu.edu.iqDepartment of MathematicsCollege of EducationUniversity of AL-QadisiyhahAl-Qadisiyhah, Iraq0000-0002-4705-6349View full profile →

* Corresponding author · click or hover a name for details

pp. 1287–1301Vol. 26Issue 6September 2023DOI: 10.47974/JIM-1627XML

Published Online:: 15 Sep 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1627
Pages:: 1287–1301

Abstract

The present paper tries to introduce a new process for solving fuzzy singular perturbation problem(SPP, s) with initial condition. This approach depends on on the partially fuzzy neural network to find the numerical solution of the second order of these problems. This system’s trial solution is written as a sum of two parts. The first section meets the fuzzy initial condition and does not have any fuzzy free parameters. The second component consists of a partially fuzzy feed-forward neural network. containing fuzzy adjustable parameters (the fuzzy weights). As a result, the starting condition is fulfilled by construction, and the network is trained to solve the differential equations. When compared to other numerical techniques, this technique proves that neural networks generate solutions with high generalizability and accurateness. A number of examples are given to show the proposed plan.

Keywords

Fuzzy singular perturbation problem Partially fuzzy neural network Fuzzy trial solution Minimized error function Hyperbolic tangent activation function

Subject Classifications

(2010) 34K28

Acknowledgements

P939H89

References

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