一类模糊线性方程组的迭代算法及其误差估计

Iteration Algorithm for Solving a System of Fuzzy Linear Equation and Error Estimate

讨论模糊线性方程组X=AX+U解的存在条件及其迭代算法(其中,A是区间数为元素的n阶矩阵,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 discuss the existential condition of solution for a system of fuzzy linear equations X=AX ＋ U, and its iteration algorithm, where A is a n × n interval number matrix （i. e. the matrix made up of interval number elements）, the unknown vector X and constant U are all n dimension vectors consisting of nonnegative 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 error estimate.