Characterizing idempotent nullnorms on bounded lattices

Abstract: 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.