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.