Constructions of uni-nullnorms and null-uninorms on a bounded lattice

Recently, Wang et al. proposed the notion of a uni-nullnorm on a bounded lattice and provided two construction methods. In this paper, we point out that the first construction method is invalid since it does not always lead to a uni-nullnorm. Then we present a method to construct a uni-nullnorm on a bounded lattice via a disjunctive uninorm and a triangular norm. Making use of existing construction methods for uninorms on a bounded lattice, we derive several construction methods for uni-nullnorms, including the second construction method by Wang et al. Dually, we present a method to construct a null-uninorm on a bounded lattice via a conjunctive uninorm and a triangular conorm, as well as several derived construction methods for null-uninorms.