Closure Operators on AMV-Valued Fuzzy Sets

Many of the new L-fuzzy structures with values in a complete MV-algebra L, such as intuitionistic, neutrosophic, or fuzzy soft sets or their combinations, cannot be explicitly expressed as classical L-fuzzy sets \(X \rightarrow L\) . On the other hand, they can be transformed into \(\mathcal{F}(L)\) -fuzzy sets \(X \rightarrow \mathcal{F}(L)\) , where \(\mathcal F\) is a functor from the category of MV-algebras to the category of the so-called almost MV-algebras. We show how this transformation of the new L-fuzzy structures can be used to define in a universal way the closure operators on the powerset objects of these new L-fuzzy structures.