Solving Complex Fuzzy Linear System of Equations Using SGMRES Method S.A. SHAHZADEH FAZELI 1,2* and S. AGHAEI 1,2 1 Parallel Processing Laboratory, Yazd University, Yazd, Iran 2 Department of Computer Science, Faculty of Mathematics, Yazd University, Yazd, Iran fazeli@yazd.ac.ir Aghaei.solmaz@yahoo.com ABSTRACT The general complex fuzzy linear system is a system of linear equations with complex fuzzy coefficients. In this paper the main aim is to develop numerical procedures that would appropriately treat general complex fuzzy linear systems and solve them. For this aim, the SGMRES (simplified generalized minimal residual) method for solving complex fuzzy system of linear equations is considered. The method is discussed in detail and illustrated by solving some numerical examples and the results are compared with projection method and two iteration methods. Keywords Complex fuzzy system of linear equations, Iterative method, SGMRES method; I. INTRODUCTION Systems of simultaneous linear equations are important for studying and solving a large proportion of the problems in many topics in applied mathematics. Usually in many applications at least some of the system parameters are represented by fuzzy rather than crisp numbers. The concept of fuzzy numbers and arithmetic operations with these numbers were first introduced and investigated by L.A. Zadeh [1-2]. A general model for solving an n × n FSLE (fuzzy system of linear equation) whose coefficients matrix is crisp and the right hand side column is an arbitrary fuzzy number vector were first proposed by Friedman et al. [8] and they studied duality fuzzy linear systems in [9]. Iterative Jacobi and Gauss-Seidel methods for FSLE were presented by Allahviranloo in [11]. In many applications, such as analysis, wave functions in quantum mechanics and many physical quantities, values are complex. Therefore, the parameters are complex fuzzy numbers. For the first time in 1987, complex fuzzy number was introduced by Buckley [3-5]. International Journal of Computer Science and Information Security (IJCSIS), Vol. 14, No. 8, August 2016 885 https://sites.google.com/site/ijcsis/ ISSN 1947-5500