  Baaz's operator $\Delta$ was introduced (by Baaz) in order to extend G\"odel
logics, after that this operator was used to expand fuzzy logics by H\'ajek in
his celebrated book. These logics were called $\Delta$-fuzzy logics. On the
other hand, possibility operators were studied in the setting of \L
ukasiewicz-Moisil algebras; curiously, one of these operators coincide with the
Baaz's one. In this paper, we study the $\Delta$ operator in the context of
($n$-valued) Super-\L ukasiewicz logics. An algebraic study of these logics is
presented and the cardinality of Lindembaun-Tarski algebra with a finite number
of variables is given. Finally, as a by-product, we present an alternative
axiomatization of H\'ajek's \L ukasiwicz logic expanded with $\Delta$.
