Nullnorms on bounded lattices constructed by means of closure and interior operators

We propose a new method for constructing nullnorms on bounded lattices based on the simultaneous use of a closure operator and an interior operator. This method requires as input a given underlying t-conorm on a join sub-semilattice (depending on the closure operator), a given underlying t-norm on a meet sub-semilattice (depending on the interior operator) and an auxiliary mapping. It is shown that a nullnorm constructed by Karaçal et al. in 2015 and a nullnorm constructed by Ertuğrul in 2018 can be retrieved as special cases. We also explain how to obtain the dual results.