International Journal of Advanced and Applied Sciences
Int. j. adv. appl. sci.
EISSN: 2313-3724
Print ISSN:2313-626X
Volume 3, Issue 8 (August 2016), Pages: 36-42
Title: Numerical solution of fuzzy initial value problem (FIVP) using optimization
Authors: Ali Asghar Behroozpoor *, Ali Vahidian Kamyad, Mohammad Mehdi Mazarei
Affiliation(s):
Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, International Campus, Mashhad, Iran
http://dx.doi.org/10.21833/ijaas.2016.08.007
Abstract:
In this paper, we introduce a new approach to obtain a novel numerical solution of fuzzy initial value problem (FIVP). This technique is based on optimization problem. In fact, the optimal solution of optimization problem is approximated solution of fuzzy initial value problem. Theoretical consideration is discussed and some examples are presented to show the ability of the method for fuzzy initial value problem.
© 2016 The Authors. Published by IASE.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Fuzzy, Initial value problem, Optimization, Linear programming, Numerical solution
Article History: Received 2 June 2016, Received in revised form 13 August 2016, Accepted 16 August 2016
Digital Object Identifier: http://dx.doi.org/10.21833/ijaas.2016.08.007
Citation:
Behroozpoor AS, Vahidian Kamyad A, and Mazarei MM (2016). Numerical solution of fuzzy initial value problem (FIVP) using optimization. International Journal of Advanced and Applied Sciences, 3(8): 36-42
http://www.science-gate.com/IJAAS/V3I8/Behroozpoor.html
References:
| Abbasbandy S and Viranloo TA (2002). Numerical solutions of fuzzy differential equations by Taylor method. Computational Methods in Applied Mathematics, 2(2): 113-124. http://dx.doi.org/10.2478/cmam-2002-0006 |
||||
| Abbasbandy S, Viranloo TA, Lopez-Pouso O and Nieto JJ (2004). Numerical methods for fuzzy differential inclusions. Computers and Mathematics with Applications, 48(10): 1633-1641. http://dx.doi.org/10.1016/j.camwa.2004.03.009 |
||||
| Allahviranloo T (2004). Numerical methods for fuzzy system of linear equations. Applied Mathematics and Computation, 155(2): 493-502. http://dx.doi.org/10.1016/S0096-3003(03)00793-8 |
||||
| Allahviranloo T (2005a). Successive over relaxation iterative method for fuzzy system of linear equations. Applied Mathematics and Computation, 162(1): 189-196. http://dx.doi.org/10.1016/j.amc.2003.12.085 |
||||
| Allahviranloo T (2005b). The Adomian decomposition method for fuzzy system of linear equations. Applied Mathematics and Computation, 163(2), 553-563. http://dx.doi.org/10.1016/j.amc.2004.02.020 |
||||
| Allahviranloo T, Ahmady N and Ahmady E (2006). Two step method for fuzzy differential equations. In International Mathematical Forum, 1(17-20): 823-832. http://dx.doi.org/10.12988/imf.2006.06069 |
||||
| Allahviranloo T, Ahmady N and Ahmady E (2007). Numerical solution of fuzzy differential equations by predictor–corrector method. Information Sciences, 177(7): 1633-1647. http://dx.doi.org/10.1016/j.ins.2006.09.015 |
||||
| Bede B and Gal SG (2005). Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems, 151(3): 581-599. http://dx.doi.org/10.1016/j.fss.2004.08.001 |
||||
| Bede B and Stefanini L (2013). Generalized differentiability of fuzzy-valued functions. Fuzzy Sets and Systems, 230: 119-141. http://dx.doi.org/10.1016/j.fss.2012.10.003 |
||||
| Diamond P (2000). Stability and periodicity in fuzzy differential equations. IEEE Transactions on Fuzzy Systems, 8(5): 583-590. http://dx.doi.org/10.1109/91.873581 |
||||
| Dubios D and Prade H (1982). Towards Fuzzy Differential Calclus: Part 3, differentiation. Fuzzy Sets and Systems (8): 225-233. http://dx.doi.org/10.1016/S0165-0114(82)80001-8 |
||||
| Friedman M, Ming M and Kandel A (1998). Fuzzy linear systems. Fuzzy Sets and Systems, 96(2): 201-209. http://dx.doi.org/10.1016/S0165-0114(96)00270-9 http://dx.doi.org/10.1016/S0165-0114(97)00416-8 |
||||
| Hüllermeier E (1999). Numerical methods for fuzzy initial value problems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7(05): 439-461. http://dx.doi.org/10.1142/S0218488599000404 |
||||
| Kaleva O (1987). Fuzzy differential equations. Fuzzy Sets and Systems, 24(3): 301-317. http://dx.doi.org/10.1016/0165-0114(87)90029-7 |
||||
| Kaleva O (1990). The Cauchy problem for fuzzy differential equations. Fuzzy sets and systems, 35(3): 389-396. http://dx.doi.org/10.1016/0165-0114(90)90010-4 |
||||
| Ma M, Friedman M and Kandel A (1999). Numerical solutions of fuzzy differential equations. Fuzzy Sets and Systems, 105(1): 133-138. http://dx.doi.org/10.1016/S0165-0114(97)00233-9 |
||||
| Mizukoshi MT, Barros LC, Chalco-Cano Y, Román-Flores H and Bassanezi RC (2007). Fuzzy differential equations and the extension principle. Information Sciences, 177(17): 3627-3635. http://dx.doi.org/10.1016/j.ins.2007.02.039 |
||||
| Puri ML and Ralescu DA (1983). Differentials of fuzzy functions. Journal of Mathematical Analysis and Applications, 91(2): 552-558. http://dx.doi.org/10.1016/0022-247X(83)90169-5 |
||||
| Seikkala S (1987). On the fuzzy initial value problem. Fuzzy Sets and Systems, 24(3): 319-330. http://dx.doi.org/10.1016/0165-0114(87)90030-3 |
||||
| Vroman A, Deschrijver G and Kerre EE (2008). Using parametric functions to solve systems of linear fuzzy equations with a symmetric matrix. International Journal of Computational Intelligence Systems, 1(3): 248-261. http://dx.doi.org/10.2991/ijcis.2008.1.3.5 http://dx.doi.org/10.1080/18756891.2008.9727622 http://dx.doi.org/10.2991/jnmp.2008.1.3.5 |
||||
| Zadeh LA (1965). Fuzzy sets. Information and Control, 8(3): 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X |
||||
| Zimmermann HJ (1996). Fuzzy Control. In Fuzzy Set Theory—and Its Applications. Springer Netherlands: 203-240. http://dx.doi.org/10.1007/978-94-015-8702-0_11 |
||||