Properties of fuzzy relations powers

summary:Properties of $\sup \nolimits $-$\ast $ compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider $\sup \nolimits $-$\ast $ powers of fuzzy relations under diverse assumptions about $\ast $ operation. At first, we remind fundamental properties of $\sup \nolimits $-$\ast $ composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined. Finally, particular properties of fuzzy relations on a finite set are presented