Numerical Methods for Solving Fuzzy System of Linear Equations
Date
2017-02-02
Authors
انعيرات, لبنى لبيب احمد
Journal Title
Journal ISSN
Volume Title
Publisher
جامعة النجاح الوطنية
Abstract
We focus our attention on the analytical and numerical methods for solving the fuzzy linear system (FLS) and fully fuzzy linear system ( FFLS).
For the analytical solution of the fuzzy linear system we have presented the following methods: Friedman's proposal, S. Abbasbandy and M. Alavi method, Fuzzy Solution by Using Fuzzy Center, Algorithmic Approach, Embedding method , LU decomposition method, and LU-Decomposition method of Mansouri and Asady. The analytical methods presented for the fully fuzzy linear system include: matrix inversion method, Cramer’s rule and LU decomposition method.
For the numerical handling of the fuzzy linear system we have implemented the following techniques, namely: Iterative Jacobi method, Gauss-Sidel methods, and Successive over relaxation iterative method. For the fully fuzzy linear system we have used the Gauss -Jacobi and Gauss- Seidel methods.
To show the efficiency of these numerical techniques we have considered some numerical examples. Numerical results for both (FLS) and (FFLS) have shown to be in a closed agreement with the analytical ones.
We strongly believe that, the Successive over relaxation iterative method(SOR) is one of the most powerful numerical techniques for solving FLS in comparison with other numerical techniques. Moreover, the Gauss- Seidel method is more efficient than the Gauss –Jacobi method for solving FFLS.