Splitting iterative methods for fuzzy system of linear equations

A class of splitting iterative methods is considered for solving fuzzy system of linear equations, which cover Jacobi, Gauss–Seidel, SOR, SSOR, and their block variants proposed by others before. We give a convergence theorem for a regular splitting, where the corresponding iterative methods converge to the strong fuzzy solution for any initial vector and fuzzy right-hand vector. Two schemes of splitting are given to illustrate the theorem. Numerical experiments further show the efficiency of the splitting iterative methods.