Numerical Method For Solving Fuzzy Singular Perturbation Problems With Initial Condition
In this paper, We present a modified approach that makes use of the neuro-fuzzy system to solve fuzzy singular perturbation problems for ODEs with IC. The name of this modified approach is the modified neuro-fuzzy system method (MNFS). The foundation of this novel approach is to swap off each x in the input vector training. set = , a first-order polynomial which will be as = , . By using MNFS, it is possible to train the neural network outside of the initial and last point range by choosing training points based on the open interval (a, b). By resolving a few numerical cases and comparing the results to those calculated using different numerical techniques, we demonstrate this improved a technique and how neural networks demonstrate yield answers with accurate and strong generalization. The suggested approach is illustrated with a number of instances.
 C. Vikas , "Analysis of Back Propagation Algorithm", Vol. 2 , Issue 8, August 2013.
 J.S.R.Jang,Adaptivenetwork basedfuzzy inference systems,IEEE Transactions on Systems Man and Cybernetics
 Shuai Song,Baoyong Zhang,Xiaona Song,Yijun Zhang,Zhengqiang Zhang,Wenjie Li. Fractional-order adaptive neuro-fuzzy sliding mode H ∞ control for fuzzy singularly perturbed systems, Journal of the Franklin Institute, Elsevier, July 2019, https://doi.org/10.1016/j.jfranklin.2019.03.020.
 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
 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.
 Hans-Jiirgen, "Fuzzy set theory and its applieations" , fourth ed,1934.
 Hamid. A. J., Rabha. W. I., Shayma A. M., Amera. I. M., and Samir. B. H., "Numerical solution of Lane-Emden equation using neural network", international conference on fundamental and applied sciences, vol. 1482, pp: 414- 418, 2012.
 Rawaa F.K. & Khalid M.M. Al-Abrahemee," Neuro-fuzzy system for solving fuzzy singular perturbation problems ",Journal of Interdisciplinary Mathematics,(2022), https://doi.org/10.1080/09720502.2022.2079229.
 S. Effati, M. Pakdaman, "Artificial Neural Network Approach for Solving Fuzzy Differential Equations", Information Sciences, 180, 1434-1457, 2010.
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