Iterative solution of fuzzy linear systems

Abstract

Linear systems have important applications to many branches of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. So it is immensely important to develop numerical procedures that would appropriately treat general fuzzy linear systems (will be denoted by FLS) and solve them. In this paper firstly a general fuzzy linear system using the embedding approach, has been investigated and then several well-known numerical algorithms for solving system of linear equations such as Richardson, Extrapolated Richardson, Jacobi, JOR, Gaus †–Seidel, EGS, SOR, AOR, ESOR, SSOR, USSOR, EMA and MSOR are extended for solving FLS. The iterative methods are followed by convergence theorems and the presented algorithms are tested by solving some numerical examples. ( †Hackbusch noticed that Gauss spelling is less correct than Gaus [W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag Inc., New York, 1994 [9]].)