Editorial Board Articles Volume 2018 Volume 2017 Volume 2016 Volume 2015 Volume 2014 Volume 2013 Volume 2012 Volume 2011 Journal of Fuzzy Set Valued Analysis Volume 2014 (2014), Article ID jfsva-00190, 8 Pages doi: 10.5899/2014/jfsva-00190 On the global solution of a fuzzy linear system Tofigh Allahviranloo1 *, Arjan Skuka2, Sahar Tahvili3 1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. 2Department of Software Engineering, Faculty of Engineering, Izmir University, Izmir, Turkey. 3Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen university, Västerås-Sweden. * Correspondence author Email address: tofigh@allahviranloo.com Tel: +989123508816. Received: 21 November 2013; Accepted: 28 November 2013 Copyright © 2014 Tofigh Allahviranloo, Arjan Skuka and Sahar Tahvili. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The global solution of a fuzzy linear system contains the crisp vector solution of a real linear system. So discussion about the global solution of a n\times n fuzzy linear system A\tilde{x}=\tilde{b} with a fuzzy number vector b in the right hand side and crisp a coefficient matrix A is considered. The advantage of the paper is developing a new algorithm to find the solution of such system by considering a global solution based upon the concept of a convex fuzzy numbers. At first the existence and uniqueness of the solution are introduced and then the related theorems and properties about the solution are proved in details. Finally the method is illustrated by solving some numerical examples. Keywords: Fuzzy linear system; Algebraic solution; Fuzzy number. References S. Abbasbandy, R. Ezzati, A. Jafarian, LU decomposition method for solving fuzzy system of linear equations, Applied Mathematics and Computation, 172 (2006) 633-643. T. Allahviranloo, M. Ghanbari, E. Hghi, A. Hosseinzadeh, A note on fuzzy linear systems, Fuzzy sets and systems, 3 (2011) 1494-1498. T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Applied Mathematics and Computation, 155 (2004) 493-502. T. Allahviranloo, Successive over relation iterative method for fuzzy system of linear equation, Applied Mathematics and Computation, 162 (2005) 189-196. T. Allahviranloo, M. Afshar kermani, Solution of a fuzzy system of linear equations, Applied Mathematics and Computation, 175 (2006) 519-531. T. Allahviranloo, E. Ahmady, N. Ahmady, KH. shams Alketaby, Block jacobi two-stag method with Gauss-sidel inneriterations for fuzzy system of linear equations, Applied Mathematics and Computations, 175 (2006) 1217-1228. T. Allahviranloo, The Adomian decomposition method for fuzzy system of linear equations, Applied Mathematics and Computation, 163 (2005) 553-563. T. Allahviranloo, M. Ghanbari, On the algebraic solution of fuzzy linear systems based on interval theory, Applied mathematical modelling, 36 (11) (2012) 5360-5379. T. Allahviranloo, M. Ghanbari, Solving fuzzy linear systems by homotopy perturbation method, International Journal of Computational Cognition, 8 (2) (2010) 24-30. T. Allahviranloo, S. Salahshour, Fuzzy symmetric solution of fuzzy linear systems, Journal of Computational and Applied Mathematics, 235 (2011) 4545-4553. J. J. Buckley, Solving fuzzy equations in economics and finance, Fuzzy Sets and Systems, 48 (1992) 289-296. J. J. Buckley, Solving fuzzy equations, Fuzzy Sets and Systems, 50 (1992) 1-14. J. J. Buckley, Y. Qu, Solving systems of linear fuzzy equations, Fuzzy Sets and Systems, 43 (1991) 33-43. M. Fridman, M. Ming, A. Kandel, Fuzzy linear systems, Fuzzy sets and systems, 96 (1998) 201-209. R. Ghanbari, N. Mahdavi-Amiri, New solutions of $L$-$R$ fuzzy linear systems using ranking functions and ABS algorithms, Applied Mathematical Modelling, 34 (2010) 3363-3375. R. Ezzati, solving fuzzy linear systyems, Soft Computing, 15 (2011) 193-197. P. Sevastjanov, L. Dyomva, A new method for solving interval and fuzzy equations: linear case, 179 (2009) 925-937. Ixizhao Wang, Zimian, Zhong, Minghu, Ha, Iteration algorithms for solving a system of fuzzy linear equatins, Fuzzy Sets and Systems, 119 (2001) 121-128. Zengfeng Iian, Liangjian Hu, David Greenhalgh, Perturbation analysis of fuzzy linear systems, Information Science, 180 (2010) 4706-4713. Xu. Dong sun, Si. zong Guo, Solution to General Fuzzy linear system and Its Necessary and sufficient condition, Fuzzy Information and Engineering, 3 (2009) 317-327. R. Yager, On the lack of inverses on fuzzy arithmetic, J. Fuzzy sets and systemes, 4 (1980) 73-82.