Simulation and evaluation of fuzzy differential equations by fuzzy neural network

Applied Soft Computing Journal

Volumn 12, Issue 9, 2012, Pages 2817-2827

  Mosleh, Maryam ^a   Otadi, Mahmood ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Feedforward neural network; Fuzzy differentialequations; Fuzzy neural networks; Learning algorithm

Indexed keywords

ALGORITHM OF FUZZY; APPLICATION EXAMPLES; APPROXIMATED SOLUTIONS; FUZZY DIFFERENTIAL EQUATIONS; FUZZY WEIGHT; HYBRID METHOD; INITIAL POINT; INITIAL VALUES; NEURAL COMPUTING; NUMERICAL EXAMPLE;

DIFFERENTIAL EQUATIONS; FEEDFORWARD NEURAL NETWORKS; LEARNING ALGORITHMS; SOFT COMPUTING;

FUZZY NEURAL NETWORKS;

EID: 84863478468     PISSN: 15684946     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.asoc.2012.03.041     Document Type: Article

References (53)

1. S. Abbasbandy, J.J. Nieto, and M. Alavi Tuning of reachable set in one dimensional fuzzy differential inclusions, Chaos Solitons & Fractals 26 2005 1337 1341 (Pubitemid 40821860)
2. S. Abbasbandy, T. Allaviranloo, O. Lopez-Pouso, and J.J. Nieto Numerical methods for fuzzy differential inclusions Computers & Mathematics with Applications 48 2004 1633 1641 (Pubitemid 40608826)
3. S. Abbasbandy, and M. Otadi Numerical solution of fuzzy polynomials by fuzzy neural network Applied Mathematics and Computation 181 2006 1084 1089 (Pubitemid 44646584)
4. S. Abbasbandy, M. Otadi, M. Mosleh, Numerical solution of a system of fuzzy polynomials by fuzzy neural network, Information Sciences 178 (2008) 1948-1960.
5. G. Alefeld, and J. Herzberger Introduction to Interval Computations 1983 Academic Press New York
6. T. Allahviranloo, E. Ahmady, and N. Ahmady Nth-order fuzzy linear differential eqations Information Sciences 178 2008 1309 1324 (Pubitemid 50007793)
7. T. Allahviranloo, N. Ahmady, and E. Ahmady Numerical solution of fuzzy differential eqations by predictor-corrector method Information Sciences 177 2007 1633 1647 (Pubitemid 46127485)
8. H.Md. Azamathulla, A.Ab. Ghani, An ANFIS-based approach for predicting the scour depth at culvert outlet, ASCE, Journal of Pipeline Systems Engineering Practice 35 (2011).
9. H.Md. Azamathulla, A.Ab. Ghani, and N.A. Zakaria ANFIS based approach for predicting maximum scour location of spillway Water Management, ICE London 162 6 2012 399 407
10. H.Md. Azamathulla, C.C. Kiat, A.Ab. Ghani, Z.A. Hasan, and N.A. Zakaria An ANFIS-based approach for predicting the bed load for moderately-sized rivers Journal of Hydro-Environment Research, Elsevier & KWRA 3 2009 35 44
11. B. Bede, I.J. Rudas, and A.L. Bencsik First order linear fuzzy differential eqations under generalized differentiability Information Sciences 177 2007 1648 1662 (Pubitemid 46107427)
12. J.J. Buckley, and T. Feuring Fuzzy differential equations Fuzzy Sets and Systems 110 2000 69 77
13. S.L. Chang, and L.A. Zadeh On fuzzy mapping and control IEEE Transactions on Systems, Man and Cybernetics 2 1972 30 34
14. M. Chen, C. Wu, X. Xue, and G. Liu On fuzzy boundary value problems Information Sciences 178 2008 1877 1892
15. D. Dubois, and H. Prade Towards fuzzy differential calculus. Part 3. Differentiation, existence and uniqueness of solution for fuzzy random Fuzzy Sets and Systems 8 1982 225 233 (Pubitemid 14449675)
16. W. Fei Existence and uniqueness of solution for fuzzy random differential equations with non-lipschitz coefficients Information Sciences 177 2007 4329 4337 (Pubitemid 47069313)
17. R. Goetschel, and W. Voxman Elementary fuzzy calculus Fuzzy Sets and Systems 18 1986 31 43
18. D. Gottlieb, and S.A. Orszag Numerical analysis of spectral methods: theory and applications CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 26 SIAM, Philadelphia 1977
19. M.T. Hagan, H.B. Demuth, and M. Beale Neural Network Design 1996 PWS publishing company Massachusetts
20. Y. Hayashi, J.J. Buckley, and E. Czogala Fuzzy neural network with fuzzy signals and weights International Journal of Intelligent Systems 8 1993 527 537
21. S. Haykin Neural Networks: A Comprehensive Foundation 1999 Prentice Hall New Jersey
22. K. Hornick, M. Stinchcombe, and H. White Multilayer feedforward networks are universal approximators Neural Networks 2 1989 359 366 (Pubitemid 20609008)
23. H. Ishibuchi, K. Kwon, and H. Tanaka A learning algorithm of fuzzy neural networks with triangular fuzzy weights Fuzzy Sets and Systems 71 1995 277 293
24. H. Ishibuchi, K. Morioka, and I.B. Turksen Learning by fuzzified neural networks International Journal of Approximate Reasoning 13 1995 327 358
25. H. Ishibuchi, and M. Nii Numerical analysis of the learning of fuzzified neural networks from fuzzy if-then rules Fuzzy Sets and Systems 120 2001 281 307 (Pubitemid 32407904)
26. H. Ishibuchi, H. Okada, and H. Tanaka Fuzzy neural networks with fuzzy weights and fuzzy biases Proceedings of ICNN, vol. 93 San Francisco 1993 1650 1655 (Pubitemid 23681928)
27. H. Ishibuchi, H. Tanaka, and H. Okada Fuzzy neural networks with fuzzy weights and fuzzy biases Proceedings of 1993 IEEE International Conferences on Neural Networks 1993 1650 1655 (Pubitemid 23681928)
28. O. Kaleva Fuzzy differential equations Fuzzy Sets and Systems 24 1987 301 317
29. T. Khanna Foundations of Neural Networks 1990 Addison-Wesley Reading, MA
30. P.V. Krishnamraju, J.J. Buckley, K.D. Relly, and Y. Hayashi Genetic learning algorithms for fuzzy neural nets Proceedings of 1994 IEEE International Conference on Fuzzy Systems 1994 1969 1974
31. J.D. Lamber Computational Methods in Ordinary Differential Equations 1983 John Wiley & Sons New York
32. A. Lapedes, and R. Farber How neural nets work? D.Z. Anderson, Neural Information Processing Systems 1988 AIP pp. 442-456
33. H. Lee, and I.S. Kang Neural algorithms for solving differential equations Journal of Computational Physics 91 1990 110 131
34. T. Leephakpreeda Novel determination of differential-equation solutions: universal approximation method Computational and Applied Mathematics 146 2002 443 457
35. R.P. Lippmann An introduction to computing with neural nets IEEE ASSP Magazine 1987 4 22
36. M. Ma, M. Friedman, and A. Kandal Numerical solutions of fuzzy differential equations Fuzzy Sets and Systems 105 1999 133 138 (Pubitemid 129523994)
37. A. Malek, and R. Shekari Beidokhti Numerical solution for high order differential equations using a hybrid neural network - optimization method Applied Mathematics and Computation 183 2006 260 271 (Pubitemid 44908606)
38. A.J. Meade Jr., and A.A. Fernandez The numerical solution of linear ordinary differential equations by feedforward neural networks Mathematical and Computer Modelling 19 12 1994 1 25
39. A.J. Meade Jr., and A.A. Fernandez Solution of nonlinear ordinary differential equations by feedforward neural networks Mathematical and Computer Modelling 20 9 1994 19 44
40. M.T. Mizukoshi, L.C. Barros, Y. Chalco-Cano, H. Román-Flores, and R.C. Bassanezi Fuzzy differential equations and the extention principle Information Sciences 177 2007 3627 3635 (Pubitemid 46920529)
41. G. Papaschinopoulos, G. Stefanidou, and P. Efraimidis Existence, uniquencess and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument Information Sciences 177 2007 3855 3870 (Pubitemid 46961976)
42. P. Picton Neural Networks second ed. 2000 Palgrave Great Britain
43. M.L. Puri, and D.A. Ralescu Differentials of fuzzy functions Journal of Mathematical Analysis and Applications 91 1983 552 558
44. R. Rodriguez-Lopez Comparison results for fuzzy differential eqations Information Sciences 178 2008 1756 1779
45. D.E. Rumelhart, J.L. McClelland, and the PDP Research Group Parallel Distributed Processing, vol. 1 1986 MIT Press Cambridge, MA
46. S. Seikkala On the fuzzy initial value problem Fuzzy Sets and Systems 24 1987 319 330
47. R.J. Schalkoff Artificial Neural Networks 1997 McGraw-Hill New York
48. J. Stanley Introduction to Neural Networks third ed. 1990 Sierra Mardre
49. J. Store, and R. Bulirsch Introduction to Numerical Analysis second ed. 1993 Springer-Verlag New York
50. Wu Congxin, and Ma Ming On embedding problem of fuzzy number space, Part 1 Fuzzy Sets and Systems 44 1991 33 38
51. C. Wu, and S. Song Approximate solutions, existence and uniqueness of the cauchy problem of fuzzy differential equations J. Mathematical Analysis and Applications 202 1996 629 644 (Pubitemid 126165689)
52. L.A. Zadeh The concept of a liguistic variable and its application to approximate reasoning. Parts 1-3 Information Sciences 8 1975 199 249 301-357; 9 (1975) 43-80
53. L.A. Zadeh Is there a need for fuzzy logic? Information Sciences 178 2008 2751 2779