Migrative t-norms with respect to continuous ordinal sums

In this paper we study and characterize continuous α-migrative t-norms T with respect to a continuous t-norm T0. Depending on whether α is an idempotent element of T0 or not, the (α, T0)-migrative property restricts the ordinal sum structure of T especially “locally”, i.e., at α or around it. Outside this well-defined neighbourhood of α, the t-norm T can be arbitrary, under the only condition of keeping it continuous. The investigation exploits the ordinal sum structure of continuous t-norms and our former results related to the migrative property.