On Generating t-Norms (t-Conorms) on Some Special Classes of Bounded Lattices

In recent years, construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices have been studied extensively. This paper presents the continued study of the construction of t-norms and t-conorms on bounded lattices. We introduce new methods for constructing t-norms and t-conorms on an arbitrary bounded lattice. Furthermore, we provide illustrative examples for clarity. Subsequently, we demonstrate how our new construction methods differ from certain existing methods for the construction of t-norms and t-conorms on bounded lattices. Finally, we reveal that new construction methods can be generalized by induction to a modified ordinal sum for t-norms and t-conorms on an arbitrary bounded lattice.