The simulations of linear system of equation with a criso real coefficient matrix and a fuzzy vector play a great utility in various fields such as mathematics, physics, statistics, computer science, engineering, and social sciences. Fuzzy linear systems have deferent applications in particular in image processing, and artificial intelligence and so on. Since in many applications at least some of the system’s parameters and measurements are represented by fuzzy rather than crisp numbers, it is important to develop mathematical models and numerical methods for fuzzy linear systems [1,2]. A general model for solving an n × ???? equation of fuzzy linear system (EFLS) whose coefficients’ matrix is crisp and right hand side column is an arbitrary fuzzy vector develop by T. Allahviranloo and Friedman [1,2]. Different authors [3,4] have investigated numerical methods for solving such FSLE. Most of mentioned methods in different articles are based on numerical methods such as matrices decomposition. Specifically, in this paper we use a numerical decomposition method for solving equations of fuzzy linear system which has been rapidly growing in recent years.

The research focus includes four parts; In part 2: Begins by laying out some definitions and results on equations of fuzzy linear system (EFLS). In part 3: We apply decomposition method of solving EFLS. In part 4: A numerical application is provided and concluding remarks are drawn in the last section.
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