Further Results on Migrative Triangular Norms

Abstract

In this paper we continue our study on the migrative property of triangular norms. First we interpret this property as a particular form of the generalized associativity functional equation. This makes it easy to extend the original property, and also to characterize it with the help of a very simple equation. Then we turn back to the original notion and show two representation (construction) theorems for migrative triangular norms that are continuous. Since the migrative property excludes both idempotent and nilpotent classes, the representation is carried out by solving a functional equation for additive generators of strict t-norms. We also study cases when the construction results in a smooth generator.