Jacobi methods in solving fuzzy linear systems

Abstract

Jacobi is one of the iterative methods in solving fuzzy linear systems, but its rate of convergence is low. Therefore two iterative methods are proposed. They are Refinement of Jacobi method and Refinement of Jacobi over Relaxation method. A numerical example is given in order to show how of both methods solve fuzzy linear systems. Then a simple comparison is given to show the efficiency of the proposed methods with Jacobi method. By numerical results, both methods are valid in solving fuzzy linear systems. At the end, the proposed methods have smaller error, shorter number of iterations and rate of convergence is higher. Therefore, Refinement of Jacobi over Relaxation method is better in solving fuzzy linear systems. On the other hand, Refinement of Jacobi method is better compared to Jacobi method to solve fuzzy linear systems.