Nullnorms on bounded lattices derived from t-norms and t-conorms

Abstract

Nullnorms with an annihilator a in any point of a bounded lattice are generalizations and unifications of t-norms and t-conorms. This study continues to investigate the construction of nullnorms on bounded lattices. We propose some methods to construct nullnorms derived from t-norms and t-conorms on bounded lattices, where some sufficient and necessary conditions on theirs annihilator are required. As a by-product of these constructions, idempotent nullnorms on bounded lattices are obtained. Further, we provide some illustrative examples of the new classes of nullnorms (idempotent nullnorms) on bounded lattices.