The aim of this research is to apply a novel technique based on the embedding method to solve the $n\times n$ fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created $n\times n$ crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created $n\times n$ crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors.

中文翻译：

---

一种求解方程组模糊系统的新技术

这项研究的目的是应用一种基于嵌入方法的新技术来解决 $ñ\times ñ$ 线性方程组（FSLE）的模糊系统。通过使用此方法，可以分两步获得FSLE的强模糊数解。第一步，如果创建 $ñ\times ñ$ 脆线性系统具有非负解，模糊线性系统将具有模糊数向量解，将在第二步中通过求解另一个 $ñ\times ñ$ 清晰的线性系统。几个定理已经证明，所提出的方法的运算数量少于弗里德曼和埃扎蒂方法的运算数量。为了显示该方案的优势，提出了两种适用的算法和流程图，并通过应用它们解决了一些数值示例。此外，证明了所获得结果的一些图，这些图表明解决方案是模糊数向量。