On the singular fuzzy linear system of equations

Document Type: Research Articles

Authors

1 باشگاه پژوهشگران جوان دانشگاه آزاد یزد.

2 Department of Computer engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

Abstract

The linear system of equations Ax = b where A = [aij ] in Cn.n is a crisp
singular matrix and the right-hand side is a fuzzy vector is called a singular
fuzzy linear system of equations. In this paper, solving singular fuzzy linear
systems of equations using generalized inverses such as Drazin inverse and
pseudo-inverse are investigated.

[1] B.C.Tripathy., A. Baruah, Notlund and Riesz mean of sequences of fuzzy
real numbers, Applied Math.Letters, 23(2010) 651-655.
[2] B.C. Tripathy, S.Borgohain, Some classes of di erence sequence spaces
of fuzzy real numbers de ned by Orlicz function, Advances in Fuzzy
Systems,( 2011) Article ID216414, 6pages.
[3] B.C.Tripathy, M.Sen and S.Nath, I-Convergence in probabilistic Nnormed
space, Soft Comput, 2012, 16, 1021-1027, DOI 10.1007/s00500-
011-0799-8.
[4] B.C.Tripathy, P.C.Das, On Convergence of seriries of fuzzy real numbers
, J.Kuwait J Sci Eng, 39(1A)(2012) 57-70.

[5] B.C.Tripathy, B.Sarma, I-Convergence double sequences of fuzzy real
numbers, Kyungpook Math Journal, 52(2)(2012) 189-200.
[6] B.C.Tripathy, A.Baruah ,M. Et and M.Gungor , On almost statistical
convergence of new type o generalized di erence sequence of fuzzy
number, Iranian Journal of Science and Technology, Transacations A:
Science , 36(2)(2012) 147-155.
[7] B.C.Tripathy, G.C.Ray, On Mixed fuzzy topological spaces and
countability, Soft Computing, 16(10)(2012) 1691-1695.
[8] S.Abbasbandy, R.Ezzati, A.Jafarian, LU decomposition method for
solving fuzzy symmetric positive de nite system of linear equations,
Appl.Math.Comp, 172 (2006), 633-643.
[9] M.Friedman, M.Ming,A. Kandel, Fuzzy Linear Systems, Fuzzy Sets and
Systems, 96(1998), 201-209.
[10] S.M.Hashemi, M. K.Mirnia, S.Shahmorad, Solving fuzzy linear system by
using the Schur complement when coecient matrix is an M-Matrix, IJFS,
5 (2008) , 15-30.
[11] S.Abbasbandy, M.Amirfakhrian, Approximation of fuzzy functions by
distance method, Mathematics Scienti c Journal(Islamic Azad University-
Arak Branch),2( 2006), 15-28.
[12] T.Allahviranloo, The adomain decomposition methods for solving fuzzy
systems of linear equations, Applied Mathematics and Computation, 163
(2005), 553-563,
[13] A.M.Al-Dubiban,S.M.El-Sayed, On the Positive De nite Solutions of the
Nonlinear Matrix Equation XA*XsAB*XtB = I, Communications in
numerical analysis,(2012), IDcna00116.
[14] A.Jafarian,S. Measoomy Nia, Utilizing a new feed-back fuzzy neural
network for solving a system of fuzzy equations , Communications in
Numerical Analysis, (2012), IDcna-00096.
[15] S.Abbasbandy, M.Otadi, M.Mosleh, Minimal solution of general dual
fuzzy linear systems, Chaos, Solutions and Fractals, 37 (2008) ,1113-1124.
[16] B.Asady, P.Mansouri, Numerical Solution of Fuzzy Linear Systems ,
International journal computer mathematics ,86( 2009),151-162.

[17] R.Ezzati, Solving fuzzy linear systems, Soft Comput , (2010)DOI
10.1007/s00500-009-0537-7.
[18] M.Nikuie, M.K. Mirnia, Normal equations for singular fuzzy linear
systems, Journal of Mathematical Extension, 6(1)(2012) 29-42.
[19] S.Campbell ,C.Meyer, Generalized Inverses of Linear Transformations,
Pitman London,1979.
[20] M.Nikuie, M.K.Mirnia, A method for solving singular linear system of
equations, Appl Math Islamic Azad University-Lahijan Branch, 7(2)(2010)
79-90.
[21] B.Detta, Numerical Linear Algebra and Application, Thomson, 1994.
[22] M.Nikuie, M.K.Mirnia, On the consistency of singular fuzzy linear system
of equations, 41th Iranian International Conference on Mathematics, 2010.
[23] S.Abbasbandy, M.Alavi, A new method for solving symmetric fuzzy linear
systems, Mathematics Scienti c Journal(Islamic Azad University Arak
Branch), 1(2005) 55-62.
[24] M.Saravi,E. Babolian, M.Rastegari, Systems of linear di erential
equations and collocation method , Mathematics Scienti c Journal(Islamic
Azad University-Arak Branch),5(2010) 79-87.
[25] L.Zheng, A characterization of the Drazin inverse, Linear Algebra and its
Application, 335 (2001) 183-188.
[26] M.Nikuie, M.K. Mirnia, Mahmoudi.Y., Some results about the index
of matrix and Drazin inverse, Math Sci. Islamic Azad University-Karaj
Branch,4(3)(2010), 283-294.
[27] D.Kincaid, W.Cheney, Numerical analysis mathematics of scienti c
Computing California,1990.
[28] K.Ho man, R.Kunze, Linear algebra, Prentice-Hall,1971.