关于Fuzzy矩阵的广义逆

On Generalized Inverse of Fuzzy Matrices

本文分别给出了Fuzzy矩阵存在广义{1,3}-逆、广义{1,4}-逆以及Moore-Penrose广义逆Fuzzy矩阵的一些充要条件。又得到求上述广义逆Fuzzy矩阵的一些公式。主要的结果有: 1.Fuzzy矩阵A的广义{1,3}-逆A^((1.3))(广义{1,4}-逆A^((1.4))存在的充要条件是Fuzzy关系方程有解。2.Fuzzy矩阵A的Moore-Penrose广义逆A^T存在的充要条件是Fuzzy关系方程均有解。3.如果B、C分别为Fuzzy关系方程的一个解,那么。

In this paper, we discuss the generalized {1, 3}-inverse, the generalized {1, 4}-inverse and Moore-Penrose generalized inverse of the Fuzzy matrices. We give the main following results. 1. For Fuzzy matrix A, there exists the generalized {1, 3}-inverse A^(1, 3) and the generalized {1, 4}-inverse A^(1, 4) if and only if Fuzzy relation equations X·A^T·A=A and A·A^T·Y=A have solution respectively. 2. For Fuzzy matrix A, there exists Moore-Penrose generalized inverse A^+ if and only if Fuzzy relation equation X·A·A^T=A and A·A^T·Y=A have solution. 3. If B, C arc the solution of Fuzzy relation equations X·A^T·A=A and A·A·~TY=A respectively, then A^+=A^T·C·B^T=C^T·A·B^T=C^T·B·A^T.