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Let X be a complete residuated lattice. Let SetRðXÞ be the category of sets with similarity relations with values in X (called X-sets), which is an analogy of the category of classical sets with relations as morphisms. A fuzzy set in an X-set in the category SetRðXÞ is a morphism from X-set to a special X-set ðX; $Þ; where $ is the biresiduation operation in X: In the paper, we prove that fuzzy sets in X-sets in the category SetRðXÞ can be expressed equivalently as special cut systems ðC a Þ a2X

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Using the theory of monads in categories and the theory of monadic relations, the concept of general transformation operator defined by a monadic relation is introduced. It is proven that a number of standard relations used in categories of fuzzy structures are monadic relations for monads defined in these categories. It is also proven that a number of standardly used transformation operators in fuzzy sets, fuzzy rough sets, or fuzzy soft sets are in the form of general operators defined by monadic relations.