Compositions of fuzzy relations with hedges II

We continue our previous paper and explore an extension of compositions of fuzzy relations. The extension consists in modifying the standard formulas for composition by particular unary functions on the set of truth degrees. We study fuzzy relational equations using the new composition operators. As a particular example, the new operators lead to a decomposition of a fuzzy relation into a crisp relation and a fuzzy relation. We provide solvability criteria for several types of fuzzy relational equations. In addition, we present a connection between the new compositions and a particular type of data dependencies.