Cancellation laws for triangular norms on product lattices

Abstract

As a continuation of the study for the direct product decomposition of t-norms on product lattices, the uniqueness of decompositions in the sense of isomorphisms should be considered. In the present paper, we concretely discuss the uniqueness of decompositions with a common factor and obtain some cancellation properties. Moreover, based on the results of t-norm homomorphisms, the decomposition of t-norm automorphisms on product lattices is also discussed.