This paper continues to study the construction of nullnorms on bounded lattices. We first propose two new construction methods of nullnorms derived from an arbitrary t norm (resp. an arbitrary t-conorm) using a closure operator (resp. an interior operator) on bounded lattices, where some sufficient and necessary conditions are considered. Then, we introduce two other methods to obtain nullnorms based on a closure operator (an interior operator) on bounded lattices with some constraints. In particular, we obtain some new classes of idempotent nullnorms on bounded lattices. Moreover, we provide some examples for a better understanding of new classes of nullnorms on bounded lattices. (C) 2021 Elsevier Inc. All rights reserved.