This paper presents a method for solving fuzzy linear systems, where the coefficient matrix is an \(n\times n\) real matrix, using a block structure of the Core inverse, and we use the Hartwig–Spindelböck decomposition to obtain the Core inverse of the coefficient matrix A. The aim of this paper is twofold. First, we obtain a strong fuzzy solution of fuzzy linear systems, and a necessary and sufficient condition for the existence strong fuzzy solution of fuzzy linear systems are derived using the Core inverse of the coefficient matrix A. Second, general strong fuzzy solutions of fuzzy linear systems are derived, and an algorithm for obtaining general strong fuzzy solutions of fuzzy linear systems by Core inverse is also established. Finally, some examples are given to illustrate the validity of the proposed method.

中文翻译：

---

用广义逆的块表示来求解模糊线性系统：核心逆

本文提出了一种求解模糊线性系统的方法，其中系数矩阵是一个\（n × n \）实矩阵，使用Core逆的块结构，我们使用Hartwig-Spindelböck分解获得Core逆。系数矩阵A的平方。本文的目的是双重的。首先，我们获得了模糊线性系统的一个强模糊解，并利用系数矩阵A的Core逆得到了存在模糊线性系统的一个强模糊解的充要条件。。其次，推导了模糊线性系统的一般强模糊解，并建立了通​​过Core逆获得模糊线性系统的一般强模糊解的算法。最后，通过一些例子说明了该方法的有效性。