一类模糊数系数矩阵的模糊线性方程组的迭代算法

Iteration Algorithm for Solving a System of Fuzzy Liner Equations with Fuzzy Number Coefficients Matrix

讨论模糊线性方程组X=A^X+U解的存在条件及其迭代算法(其中,A~是以模糊数为元素的n×n矩阵,未知量X和常量U都是以模糊数为元素的n维向量,并且其加法和乘法均由Zadeh的扩张原理定义)。首先研究解的存在条件,尔后探讨求解的迭代算法及误差估计。

This paper diccuss the existential condition of solution for a system of fuzzy linear equations X = AX＋U, and its iteration algorithm, where A is a n X n fuzzy numbers matrix, the unknown vector X and the constant U are all n dimension vectors sonsisting of fuzzy numbers, and the addition and multiplication are defined by Zadeh＇s extension principle. Firstly we study the existential condition of solution, then discuss the iteration algorithm and erroe estimation.