模糊矩阵的特征向量

Eigenvectors of Fuzzy Matrices

设 A为 n阶模糊方阵 ,X为 n维模糊向量 .若模糊矩阵方程 AX =X成立 ,则称 X为模糊矩阵 A的一个特征向量 .本文给出了模糊向量 X为模糊矩阵 A的特征向量的充分必要条件 ,最大特征向量的求法 ,并建立了布尔方阵特征向量个数的计算公式 .

Let A be an n × n fuzzy matrix, X be an n\|tuple fuzzy vector. X is called a eigenvector of A if AX=X. In this paper, a theoretical necessary and sufficient condition has been established for X to be a eigenvector of A. It is shown that how to calculate the maximal eigenvector of A. And the formula to calculate the number of eigenvetors of A has been established when A is a Boolean square matrix.