Construction methods for the smallest and largest uni-nullnorms on bounded lattices

This paper continues to study the construction of uni-nullnorms on bounded lattices. At first, we introduce a new method for constructing the smallest uni-nullnorm on an arbitrary bounded lattice L having the elements e , a ∈ L , based on the existence of a uninorm on [ 0 , a ] 2 with the neutral element e and a triangular norm on [ a , 1 ] 2 . And then, we propose another new approach to obtain the largest uni-nullnorm on L via a uninorm on [ 0 , a ) 2 with the neutral element e and a triangular norm on [ a , 1 ] 2 . Furthermore, we provide some corresponding examples to illustrate that our construction methods differ from the existing ones.