CANONICAL FORM OF AN TRANSITIVE INTUITIONISTIC FUZZY MATRICES

CANONICAL FORM OF AN TRANSITIVE INTUITIONISTIC FUZZY MATRICES

Some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive fuzzy matrix is given using the properties. As a special case an open problem concerning idempotent matrices is solved. Thus we have the same result in a intuitionistic fuzzy matrix theory. In our results a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix play an important role. We decompose a transitive intuitionistic fuzzy matrix into sum of a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix. Then we obtain a canonical form of the transitive intuitionistic fuzzy matrix.