  This paper deals with the problem of finding the preferred extensions of an
argumentation framework by means of a bijection with the naive sets of another
framework. First, we consider the case where an argumentation framework is
naive-bijective: its naive sets and preferred extensions are equal. Recognizing
naive-bijective argumentation frameworks is hard, but we show that it is
tractable for frameworks with bounded in-degree. Next, we give a bijection
between the preferred extensions of an argumentation framework being
admissible-closed (the intersection of two admissible sets is admissible) and
the naive sets of another framework on the same set of arguments. On the other
hand, we prove that identifying admissible-closed argumentation frameworks is
coNP-complete. At last, we introduce the notion of irreducible self-defending
sets as those that are not the union of others. It turns out there exists a
bijection between the preferred extensions of an argumentation framework and
the naive sets of a framework on its irreducible self-defending sets.
Consequently, the preferred extensions of argumentation frameworks with some
lattice properties can be listed with polynomial delay and polynomial space.
