The main purpose of this paper is to solve a dual fuzzy linear system algebraically. In considered systems, the coefficient matrices are crisp-valued matrices and the left and right hand sides vectors are fuzzy number-valued vectors. Two types of solutions are defined and the relationship between them is investigated. Finally, based on the obtained results, a simple method is presented to obtain a unique algebraic solution of a dual fuzzy linear system. The main advantage of the proposed method over existing methods is that it does not need to convert a dual fuzzy linear system to two crisp linear systems. Also, a new necessary and sufficient condition for the existence of unique algebraic solution of a dual fuzzy linear system is presented. To illustrate our method, two numerical examples and an applied example in economy are given.

本文的主要目的是用代数方法求解一个对偶模糊线性系统。在所考虑的系统中，系数矩阵是清晰值矩阵，左侧和右侧向量是模糊数值向量。定义了两种类型的解决方案，并研究了它们之间的关系。最后，基于所得结果，提出了一种简单的方法来获得对偶模糊线性系统的唯一代数解。与现有方法相比，所提出的方法的主要优点是它不需要将双模糊线性系统转换为两个清晰的线性系统。同时，提出了一个对偶模糊线性系统唯一代数解存在的新的充要条件。为了说明我们的方法，给出了两个数值例子和一个经济应用例子。