Anewperspective on constructing 2-uninorms on bounded lattices
Yaming Wang, Yiqun Zhang, Huawen Liu · Filomat · 2024
Recently, Ertu?rul provided a way to obtain a 2-uninorm on a bounded lattice L by using a disjunctive uninorm and a conjunctive uninorm. Later, Xie and Yi proposed two methods for constructing 2-uninorms on L by using two uninorms U1 on [0L,k] and U2 on [k,1L], and showed that the function constructed by the first method is a 2-uninorm iff U2 is conjunctive and the function constructed by the second method is a 2-uninorm iff U1 is disjunctive. Motivated by the three methods, we present two approaches to construct a 2-uninorm on L via a uni-nullnorm and a t-conorm (a t-norm and a null-uninorm). By the first new one, we can obtain a 2-uninorm on L such that the uninorm on [0L, k] is not necessarily disjunctive and the uninorm on [k, 1L] is not necessarily conjunctive. The second approach is different from all existing construction ways for 2-uninorms on L.