On reduction of transitive fuzzy matrices and its applications (Q1310404)

For fuzzy matrices (matrices having values in the closed interval \(\langle 0,1 \rangle)\) the operations of addition, multiplication, transpose of a matrix and powers of a square matrix are defined. A fuzzy matrix \(R\) is called max-min transitive iff \(R^ 2 \leq R\), \(w\)- transitive iff \(R^ 2=R\) and \(s\)-transitive iff \(r_{ik}>r_{ki}\) and \(r_{kj}>r_{jk}\) imply \(r_{ij}>r_{ji}\) for any \(i,j,k\) such that \(i \neq j\), \(j \neq k\), \(i \neq k\). The class of the \(s\)-transitive (resp. \(w\)-transitive) fuzzy matrices contains properly the class of the max-min transitive fuzzy matrices for which reduction models are already known. It is shown that some basic properties of these models remain valid also for \(s\)-transitive (resp. \(w\)-transitive) fuzzy matrices.