Representation of uni-nullnorms and null-uninorms on bounded lattices

In this paper, we present the representation for uni-nullnorms with disjunctive underlying uninorms on bounded lattices.It is shown that our method can cover the representation of nullnorms on bounded lattices and some of existing construction methods for uni-nullnorms on bounded lattices.Illustrative examples are presented simultaneously.In addition, the representation of null-uninorms with conjunctive underlying uninorms on bounded lattices is obtained dually.