Modification Fuzzy Artificial Neural Networks For Solving Fuzzy Singular Perturbation Problems With Boundary Condition
DOI:
https://doi.org/10.29304/jqcm.2023.15.1.1149Keywords:
Singular perturbation problem., Neuro – fuzzy system., Minimized Error Function., Hyperbolic Tangent Activation FunctionAbstract
Throughout this work through the using of a neuro-fuzzy system, we have developed a new technique. This updated approach is known neuro – fuzzy system method (MNFS). to develop a numerical method for resolving (FSPPs) for ordinary differential equations with BC. The activation function for hyperbolic tangents used to determine the hidden units' sigmoid function and the parameters of a fuzzy neural network and its formula is: .Standard training algorithms and analytical techniques were contrasted with the suggested strategy. Our research revealed the provided approach stands out for its excellent accuracy of the results, low error rate, and much faster speed than that of conventional methods. A number of examples are used to demonstrate the suggested strategy.
Downloads
References
2009,https://doi.org/10.1016/B978-044452701-1.00128-9
[2] K.V. Shihabudheen,G.N. Pillai," Knowledge-Based Systems ", Elsevier
15 July 2018,https://doi.org/10.1016/j.knosys.2018.04.014
[3] Ali M. H.,"Design Fast Feed-Forward Neural Networks to Solve Two
Point Boundary Value Problems", M.Sc. Thesis, College of Education Ibn
Al-Haitham,University of Baghdad, Iraq, 2012.
[4] Hussein A. A. T., "Design Fast Feed-Forward Neural Networks to Solve
Singular Boundary Value Problems", M.Sc. Thesis, College of Education Ibn
Al-Haitham,University of Baghdad, Iraq, 2013.
[5] Tawfiq L. N. M., Al-Abrahemee K. M. M.,"Design Neural Network to
Solve Singular Perturbation Problems", Applied and Computational
Mathematics, Vol. 3, No. 3, 1-5, 2014 .
[6] K.M.M. Al-Abrahemee. Modification of high performance training algorithm for solving singular perturbation partial differential equations with cubic convergence, Journal of Interdisciplinary Mathematics, 24(7), 2035-2047, (2021) https://doi.org/10.1080/09720 502.2021.2001136
[7] Russul Kareem & Khalid M.M. Al-Abrahemee, Modification artificial neural networks for solving singular perturbation problems'Journal of Interdisciplinary Mathematics,(2022), https://doi.org/10.1080/09720502.2022.2072063.
[8] Zadeh, L. A., “Fuzzy Sets”, In Fuzzy Sets and Applications: Selected papers by L. A. Zadeh, Edited by Yager R. R., Ovehinnikos S., Tong R.M. and Ngnyen W.T., John Wiely and Sons, Inc., 1987.
[9] Dubois, D. and Prade, H., “Fuzzy Sets and Systems; Theory and Applications”, Academic Press, Inc., 1980.
[10] Yan, J., Ryan, M. and Power, J., “Using Fuzzy Logic: Towards Intelligent Systems”, Prentice Hall, Inc., 1994.
[11] Al-Doury, N. E., “Application of Fuzzy Set Theory in Character Cursive Recognition”, M.Sc. Thesis, College of Education, Ibn Al-Haitham, University of Baghdad, 2002.
[12] S. Effati, M. Pakdaman, "Artificial Neural Network Approach for Solving Fuzzy Differential Equations", Information Sciences, 180, 1434-1457, 2010.
