Element-Oriented Construction Methods for Nullnorms on Bounded Lattices

Nullnorms are aggregation functions with an annihilator and are generalizations of t-norms and t-conorms. After the introduction of the concept of nullnorms on bounded lattices by Karaçal et al., the studies on their construction methods in such structures have been initiated. Following the paper of Karaçal and Şanlı, in which proposed element-based construction methods for t-norms and t-conorms on bounded lattices, a natural research question emerged: Are there any element-based construction methods for nullnorms on a bounded lattice L? In this paper, we address this question and propose construction methods for nullnorms with an annihilator element $k\in L\setminus \{0,1\}$, depending on an element $\eta \in L\setminus \{0,k,1\}$, by examining the relationship between $\eta$ and k. The proposed methods are compared with some existing approaches in the literature and are shown to be distinct. These theoretical findings are further supported with illustrative examples.