Transitivity and subinverses in fuzzy matrices (Q1311713)

For fuzzy matrices (matrices having values in the closed interval \(\langle 0,1 \rangle)\) the relation \(A \leq B\) is defined iff \(a_{ij} \leq b_{ij}\) for all \(i,j\). If \(R^ 2 \leq R\), then \(R\) is called transitive. If for a fuzzy matrix \(A\) there exists a fuzzy matrix \(B\) such that \(ABA \leq A\), then \(B\) is called a subinverse of \(A\). The authors present necessary and sufficient conditions for a fuzzy matrix to be transitive and give some criteria for subinverses of a transitive fuzzy matrix.