SOLVING FUZZY LINEAR SYSTEMS IN THE STOCHASTIC ARITHMETIC BY APPLYING CADNA LIBRARY

Mohammad Ali Fariborzi Araghi, Hassan Fattahi

Abstract

In this paper, a fuzzy linear system with crisp coefficient matrix is considered in order to solve in the stochastic arithmetic. The fuzzy CESTAC method is applied in order to validate the computed results. The Gauss-Seidel and Jacobi iterative methods are used for solving a given fuzzy linear system. In order to implement the proposed algorithm, the CADNA library is applied to find the optimal number of iterations. Finally, two numerical examples are solved based on the given algorithm in the stochastic arithmetic.

References

  1. Abbasbandy, S., Ezzati, R. and Jafarian, A. (2006). LU decomposition method for solving fuzzy system of linear equations, Appl. Math. Comput., 172, 633-643.
  2. Abbasbandy, S. and Fariborzi Araghi, M. A. (2004). The use of the Stochastic arithmetic to estimate the value of interpolation polynomial with optimal degree, Appl. Num. Math., 50, 279-290.
  3. Allahviranloo, T. (2004). Numerical methods for fuzzy system of linear equations, Appl. Math. Comput., 155, 493-502.
  4. Allahviranloo, T. (2005). Successive overrelaxation iterative fuzzy system of linear equations, Appl. Math. Comput., 162, 189-196.
  5. Chesneaux, J. M. (1992). Stochastic arithmetic properties, Comput. and Applied Mathematics, IMACS, 81-89.
  6. Dehghan, M. and Hashemi, B. (2006). Iterative solution of fuzzy linear systems, Appl. Math. Comput., 175, 645- 674.
  7. Freidman, M., Ming, M. and Kandel, A. (1998). Fuzzy linear systems, Fuzzy Sets & Systems, 96, 201-209.
  8. Fariborzi Araghi, M. A. (2008). Dynamical control of accuracy using the stochastic arithmetic to estimate double and improper integrals, Math. and Com. Appl., 13(2), 91-100.
  9. Jezequel, F. and Chesneaux, J. M. (2008). CADNA, a library for estimating round-off error propagation, Comp. Phys. Commun., 178, 933-955.
  10. Khojasteh Salkuyeh, D. and Toutounian, F. (2006). Numerical accuracy of a certain class of iterative methods for solving linear system, Appl. Math. and Comp., 176, 727-738.
  11. Vignes, J. (1993). A stochastic arithmetic for reliable scientific computation, Math. and Comp. in Simul., 35, 233-261.
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Paper Citation


in Harvard Style

Fariborzi Araghi M. and Fattahi H. (2011). SOLVING FUZZY LINEAR SYSTEMS IN THE STOCHASTIC ARITHMETIC BY APPLYING CADNA LIBRARY . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011) ISBN 978-989-8425-83-6, pages 446-450. DOI: 10.5220/0003675804460450


in Bibtex Style

@conference{fcta11,
author={Mohammad Ali Fariborzi Araghi and Hassan Fattahi},
title={SOLVING FUZZY LINEAR SYSTEMS IN THE STOCHASTIC ARITHMETIC BY APPLYING CADNA LIBRARY},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011)},
year={2011},
pages={446-450},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003675804460450},
isbn={978-989-8425-83-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011)
TI - SOLVING FUZZY LINEAR SYSTEMS IN THE STOCHASTIC ARITHMETIC BY APPLYING CADNA LIBRARY
SN - 978-989-8425-83-6
AU - Fariborzi Araghi M.
AU - Fattahi H.
PY - 2011
SP - 446
EP - 450
DO - 10.5220/0003675804460450