Refined Generalized Iterative Methods in Solving Fully Fuzzy Linear Systems

Abstract

The system of linear equations plays a major role in various areas of sciences, such as mathe matics, physics, statistics, engineering and social sciences. These are important for studying and solving a large proportion of the problems in many topics in applied mathematics. Usually, in many applications, all the system’s parameters are represented by fuzzy rather than crisp numbers, and hence it is important to develop mathematical models and numerical procedures that would appro priately treat general fully fuzzy linear systems(FFLS) and solve them. In this study, the refined iterative methods namely, refinement of generalized Jacobi (RGJ) and refinement of generalized Gauss-Seidel (RGGS) methods for solving FFLS of equations are studied. A description of these numerical iterative methods and their convergence properties has been presented. The efficiency of the proposed methods were demonstrated by solving different test problems. The result presented in tables and graphs shows that RGJ and RGGS methods converge if the crisp coefficient matrix Ax=b derived from the corresponding FFLS of equations is diagonally dominant for any initial vectors. Based on the numerical results, one can realize that the proposed methods are well suited for solving FFLS and enable one to obtain more accurate solutions. Therefore, we came to the conclusion that the proposed methods are much more promising, efficient, and powerful than other methods in terms of providing relatively with very small errors.