Abstract
Predicting the solution of complex systems is a significant challenge. Complexity is caused mainly by uncertainty and nonlinearity. The nonlinear nature of many complex systems leaves uncertainty irreducible in many cases.
In this work, a novel iterative strategy based on the feedback neural network is recommended to obtain the approximated solutions of the fully fuzzy nonlinear system (FFNS). In order to obtain the estimated solutions, a gradient descent algorithm is suggested for training the feedback neural network. An example is laid down in order to demonstrate the high accuracy of this suggested technique.
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References
Jafari, R., Yu, W.: Fuzzy control for uncertainty nonlinear systems with dual fuzzy equations. J. Intell. Fuzzy. Syst. 29, 1229–1240 (2015)
Jafari, R., Yu, W., Li, X.: Fuzzy differential equation for nonlinear system modeling with Bernstein neural networks. IEEE Access. (2017). https://doi.org/10.1109/ACCESS.2017.2647920
Jafari, R., Yu, W.: Uncertainty nonlinear systems modeling with fuzzy equations. Math. Probl. Eng. 2017 (2017). https://doi.org/10.1155/2017/8594738
Jafari, R., Yu, W.: Uncertainty nonlinear systems modeling with fuzzy equations. In: Proceedings of the 16th IEEE International Conference on Information Reuse and Integration, San Francisco, Calif, USA, pp. 182–188, August 2015
Jafari, R., Yu, W., Li, X.: Numerical solution of fuzzy equations with Z-numbers using neural networks. Intell. Autom. Soft Comput. 1, 1–7 (2017)
Jafari, R., Yu, W., Li, X., Razvarz, S.: Numerical solution of fuzzy differential equations with Z-numbers using Bernstein neural networks. Int. J. Comput. Intell. Syst. 10, 1226–1237 (2017)
Razvarz, S., Jafari, R., Yu, W.: Numerical solution of fuzzy differential equations with Z-numbers using fuzzy Sumudu Transforms. Adv. Sci. Technol. Eng. Syst. J. 3, 66–75 (2018)
Razvarz, S., Jafari, R., Granmo, O.-Ch., Gegov, A.: Solution of dual fuzzy equations using a new iterative method. In: Nguyen, N.T., Hoang, D.H., Hong, T.-P., Pham, H., Trawiński, B. (eds.) ACIIDS 2018. LNCS (LNAI), vol. 10752, pp. 245–255. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75420-8_23
Pratama, M., Lu, J., Anavatti, S.G., Lughofer, E., Lim, C.P.: An incremental meta-cognitive-based scaffolding fuzzy neural network. Neurocomputing 171, 89–105 (2016)
Pratama, M., Lu, J., Lughofer, E., Zhang, G., Er, M.J.: Incremental learning of concept drift using evolving type-2 recurrent fuzzy neural network. IEEE Trans. Fuzzy Syst. 25, 1175–1192 (2017)
Abiyev, R.H., Kaynak, O.: Fuzzy wavelet neural networks for identification and control of dynamic plantsa novel structure and acomparative study. IEEE Trans. Ind. Electron. 55, 3133–3140 (2008)
Hornik, K.: Approximation capabilities of multilayer feed-forward networks. Neural Netw. 4, 251–257 (1991)
Scarselli, F., Tsoi, A.C.: Universal approximation using feedforward neural networks: a survey of some existing methods, and some new results. Neural Netw. 11, 15–37 (1998)
Ishibuchi, H., Kwon, K., Tanaka, H.: A learning of fuzzy neural networks with triangular fuzzy weghts. Fuzzy Sets Syst. 71, 277–293 (1995)
Hayashi, Y., Buckley, J.J., Czogala, E.: Fuzzy neural network with fuzzy signals and weights. Int. J. Intell. Syst. 8, 527–537 (1993)
Buckley, J.J., Eslami, E.: Neural net solutions to fuzzy problems: the quadratic equation. Fuzzy Sets Syst. 86, 289–298 (1997)
Mosleh, M.: Evaluation of fully fuzzy matrix equations by fuzzy neural network. Appl. Math. Model. 37, 6364–6376 (2013)
Abbasbandy, S., Otadi, M.: Numerical solution of fuzzy polynomials by fuzzy neural network. Appl. Math. Comput. 181, 1084–1089 (2006)
Jafarian, A., Jafari, R.: Approximate solutions of dual fuzzy polynomials by feed-back neural networks. J. Soft Comput. Appl. (2012). https://doi.org/10.5899/2012/jsca-00005
Takagi, T., Sugeno, M.: Identification of systems and its applications to modeling and control. IEEE Trans. Man Cybern. 15, 116–132 (1985)
Lughofer, E., Cernuda, C., Kindermann, S., Pratama, M.: Generalized smart evolving fuzzy systems. Evolv. Syst. 6, 269–292 (2015)
Angelov, P.P., Filev, D.: An approach to online identification of Takagi-Sugeno fuzzy models. IEEE Trans. Syst. Man Cybern. Part B Cybern. 34, 484–498 (2004)
Chen, G., Pham, T.T., Weiss, J.J.: Modeling of control systems. IEEE Aerosp. Electron. Syst. 31, 414–428 (1995)
Abbasbandy, S., Ezzati, R.: Homotopy method for solving fuzzy nonlinear equations. Appl. Sci. 8, 1–7 (2006)
Mouzouris, G.C., Mendel, J.M.: Dynamic non-singleton logic systems for nonlinear modeling. IEEE Trans. Syst. 5, 199–208 (1997)
Allahviranloo, T.: The Adomian decomposition method for fuzzy system of linear equations. Appl. Math. Comput. 163, 553–563 (2005)
Paripour, M., Zarei, E., Shahsavaran, A.: Numerical solution for a system of fuzzy nonlinear equations. J. Fuzzy Set Valued Anal. 2014, 1–10 (2014)
Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) an outline. Inform. Sci. 172, 1–40 (2005)
Alefeld, G., Herzberger, J.: Introduction to Interval Computations. Academic Press, New York (1983)
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Jafari, R., Razvarz, S., Gegov, A. (2018). A New Computational Method for Solving Fully Fuzzy Nonlinear Systems. In: Nguyen, N., Pimenidis, E., Khan, Z., Trawiński, B. (eds) Computational Collective Intelligence. ICCCI 2018. Lecture Notes in Computer Science(), vol 11055. Springer, Cham. https://doi.org/10.1007/978-3-319-98443-8_46
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