  Nullnorms with a zero element being at any point of a bounded lattice are an
important generalization of triangular norms and triangular conorms. This paper
obtains an equivalent characterization for the existence of idempotent
nullnorms with the zero element $a$ on any bounded lattice containing two
distinct elements incomparable with $a$. Furthermore, some basic properties for
the bounded lattice containing two distinct element incomparable with a are
presented.
