A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.
[1] S. Abbsabandy, A. Jafarian and R. Ezzati, Conjugate gradient method
for fuzzy systematic positive definite system of linear equations, Applied
mathematics and computation 171 (2005) 1184-1191.
[2] T. Allahvirabloo, Numerical methods for fuzzy system of linear equations,
Applied mathematics and computation 155 (2004) 493-502.
[3] T. Allahvirabloo, E. Ahmady, N. Ahmady and Kh. Shams Alketaby,
Block Jacobi two-stage method with Gauss-Sidel inner iterations for fuzzy
system of linear equations, Applied mathematics and computation 175
(2006) 1217-1228.
[4] J. J. Buckley and Y. Qu, Solving systems of linear fuzzy equations, Fuzzy
Sets and Systems 43 (1991) 33-43.
[5] M. Dehghan and B. Hashemi, Iterative solution of fuzzy linear systems,
Applied mathematics and computation 175 (2006) 645-674.
[6] M. Dehghan and B. Hashemi, Solution for the fully fuzzy linear systems
using the decomposition procedure, Applied Mathematics and Computation
182 (2006) 1568-1580.
[7] M. Dehghan, B. Hashemi and R. Ghatee, Computational methods for
solving fully fuzzy linear systems, Applied Mathematics and Computation
179 (2006) 328-343.
[8] M. Dehghan, B. Hashemi and R. Ghatee, Solution of the fully fuzzy linear
systems using iterative techniques, Chaos Solutions and Fractals 34 (2007)
316-336.
[9] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications,
London: Academic Press, , 1980.
[10] M. Friedman, M. Ma, A. Kandel, Fuzzy linear systems, Fuzzy sets and
systems 96 (1998) 201-209.
[11] D. M. Gay, Solving interval linear solutions, SIAM Journal of Numerical
Analysis 19 (1982) 858-870.
[12] S.-X Miao, B. Zheng and K. Wang, Block SOR methods for fuzzy linear
systems, Journal of Applied Mathematics and Computing 26 (2008) 201-
218.
[13] Y. Saad, Iterative methods for sparse linear systems, USA: SIAM, 2nd,
2000.
[14] I. Skalna, M. V. Rama Rao and A. Pownuk, Systems of fuzzy equations in
structural mechanics, Journal of computational and Applied Mathematics
218 (2008) 149-156.
[15] A. Vroman, G. Deschrijver, E. E. Kerre, Solving systems of linear fuzzy
equations by parametric functions-An improved algorithm, Fuzzy Sets
and Systems 158 (2007) 1515-1534.
[16] W.Y. Yang, W. Cao, T.-S. Chung and J. Morries, Applied Numerical
Methods Using Matlab, Jersey: John Wiley & Sons, 2005.
[1] S. Abbsabandy, A. Jafarian and R. Ezzati, Conjugate gradient method
for fuzzy systematic positive definite system of linear equations, Applied
mathematics and computation 171 (2005) 1184-1191.
[2] T. Allahvirabloo, Numerical methods for fuzzy system of linear equations,
Applied mathematics and computation 155 (2004) 493-502.
[3] T. Allahvirabloo, E. Ahmady, N. Ahmady and Kh. Shams Alketaby,
Block Jacobi two-stage method with Gauss-Sidel inner iterations for fuzzy
system of linear equations, Applied mathematics and computation 175
(2006) 1217-1228.
[4] J. J. Buckley and Y. Qu, Solving systems of linear fuzzy equations, Fuzzy
Sets and Systems 43 (1991) 33-43.
[5] M. Dehghan and B. Hashemi, Iterative solution of fuzzy linear systems,
Applied mathematics and computation 175 (2006) 645-674.
[6] M. Dehghan and B. Hashemi, Solution for the fully fuzzy linear systems
using the decomposition procedure, Applied Mathematics and Computation
182 (2006) 1568-1580.
[7] M. Dehghan, B. Hashemi and R. Ghatee, Computational methods for
solving fully fuzzy linear systems, Applied Mathematics and Computation
179 (2006) 328-343.
[8] M. Dehghan, B. Hashemi and R. Ghatee, Solution of the fully fuzzy linear
systems using iterative techniques, Chaos Solutions and Fractals 34 (2007)
316-336.
[9] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications,
London: Academic Press, , 1980.
[10] M. Friedman, M. Ma, A. Kandel, Fuzzy linear systems, Fuzzy sets and
systems 96 (1998) 201-209.
[11] D. M. Gay, Solving interval linear solutions, SIAM Journal of Numerical
Analysis 19 (1982) 858-870.
[12] S.-X Miao, B. Zheng and K. Wang, Block SOR methods for fuzzy linear
systems, Journal of Applied Mathematics and Computing 26 (2008) 201-
218.
[13] Y. Saad, Iterative methods for sparse linear systems, USA: SIAM, 2nd,
2000.
[14] I. Skalna, M. V. Rama Rao and A. Pownuk, Systems of fuzzy equations in
structural mechanics, Journal of computational and Applied Mathematics
218 (2008) 149-156.
[15] A. Vroman, G. Deschrijver, E. E. Kerre, Solving systems of linear fuzzy
equations by parametric functions-An improved algorithm, Fuzzy Sets
and Systems 158 (2007) 1515-1534.
[16] W.Y. Yang, W. Cao, T.-S. Chung and J. Morries, Applied Numerical
Methods Using Matlab, Jersey: John Wiley & Sons, 2005.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55031", author = "Hsuan-Ku Liu", title = "On the Solution of Fully Fuzzy Linear Systems", abstract = "A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.
", keywords = "Fully fuzzy linear equations, iterative method, homotopy perturbation method, approximate solutions.", volume = "4", number = "7", pages = "878-5", }
