SOME METHODS TO OBTAIN T-NORMS AND T-CONORMS ON BOUNDED LATTICES

In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice L based on a priori given t-norm acting on [a, 1] and t-conorm acting on [0, a] for an arbitrary element a is an element of L\{0, 1}. We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.