Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 6, 263 - 274 Regular Splitting Method for Approximating Linear System of Fuzzy Equation M. Mosleh and M. Otadi Department of Mathematics, Islamic Azad University Firuozkooh Branch, Firuozkooh, Iran Maryam Mosleh79@yahoo.com mahmood otadi@yahoo.com Sh. Vafaee Varmazabadi Abstract A class of splitting iterative methods are considered for solving fuzzy system of linear equations, which covers Jacobi, Gauss Seidel, SOR, SSOR and their block variance proposed. Theoretical analysis showed that for a regular splitting, the corresponding iterative method con- verge to the unique fuzzy solution for any initial vector and fuzzy right hand side vector. Finally, we illustrate our approach by some numerical examples. Keywords: Fuzzy number; Fuzzy linear system; Splitting iterative meth- ods 1 Introduction The concept of fuzzy numbers and fuzzy arithmetic operations were first introduced by Zadeh [34], Dubois and Prade [11]. We refer the reader to [22] for more information on fuzzy numbers and fuzzy arithmetic. Fuzzy systems are used to study a variety of problems ranging from fuzzy topological spaces [9] to control chaotic systems [17, 20], fuzzy metric spaces [27], fuzzy differential equations [4], fuzzy linear systems [3, 2, 8, 31] and particle physics [12, 13, 14, 15, 16, 26, 29]. One of the major applications of fuzzy number arithmetic is treating fuzzy linear systems and fully fuzzy linear systems. Several problems in various areas such as economics, engineering and physics lead to the solution of a linear system of equations. In many applications, the parameters of the system