Kybernetika

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.