求解一类模糊线性方程系统的迭代算法

Iteration Algorithms for Solving a System of Fuzzy Linear Equations

主要讨论了模糊线性方程组X=AX+U解的状态和它的重复算法,其中A为n×n实数矩阵,未知量X和常量U都是由n个模糊数组成的向量,并且其加法和数量乘法均由Zadeh的扩展原理定义.在模糊向量引入距离之后证明了如果‖A‖∞<1,该方程组就有唯一1组解.最后又引入了简单重复序列和连续重复序列并给出了其收敛性和误差估计.

The solution of fuzzy linear equations X=AX+U and its iteration algorithms are discussed,where A is a real n×n matrix,the unknown vector X and the constant U are all vectors consisting of n fuzzy numbers,and the addition,scale-multiplication are defined by Zadeh's extention principle.After introducing a metric between two fuzzy vectors,Proved that the system has unique solution if ‖A‖_∞<1.The convergence and the error estimation for using simple iteration to obtain the solution are given.Finally,The convergence and the error estimation of successive iteration sequence for obtaining the solution are given.