New family of triangular norms via contrapositive symmetrization of residuated implications

In this paper a certain transformation of triangular norms (called N-annihi lation) is studied. This problem is strongly related to the contrapositive symmetry property of residuated implications. We characterize those continu ous triangular norms where the annihilated binary operation is a triangular norm. Some surprising properties of nilpotent triangular norms are present ed e.g. the nilpotent minimum is described as limit of nilpotent triangular norms. As a consequence, a new family of triangular norms (called nilpoten t ordinal sums) owing several attractive properties is discovered. The new family contains the nilpotent biangular norms and the nilpotent minimum as extremal cases and can be admitted into investigations in the theory of Gir ard monoids as well. (C) 2000 Elsevier Science B.V. All rights reserved.