Morita-equivalence of monoids and equivalent categories of fuzzy acts over monoids

This paper considers the relations between the Morita-equivalence of two monoids on the one hand and the equivalence of the categories of fuzzy acts over these two monoids on the other hand. The main result of this work is that two monoids A and B are equivalent in the sense of Morita if and only if their categories of fuzzy-acts are equivalent. Moreover, the functors of these two equivalences are naturally related to each other.