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

Abstract

The linear system of equations Ax = b where A = [a_{ij} ] in C^{n.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.

References

[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 dierence sequence spaces of fuzzy real numbers dened 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 dierence 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 denite 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 Scientic 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 Denite 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 Scientic Journal(Islamic Azad University Arak Branch), 1(2005) 55-62. [24] M.Saravi,E. Babolian, M.Rastegari, Systems of linear dierential equations and collocation method , Mathematics Scientic 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 scientic Computing California,1990. [28] K.Homan, R.Kunze, Linear algebra, Prentice-Hall,1971.