An extension of the migrative property for triangular norms

In this paper we extend the migrative property of triangular norms by allowing an arbitrary fixed t-norm T0 in the defining equation instead of the originally used product. Equivalent forms of this extended migrativity are also provided and proved. Two particular cases when T0 is either the minimum or the Łukasiewicz t-norm are studied. In these cases all continuous extended migrative t-norms are characterized and represented. The proofs are constructive, which helps the reader to build up various families of extended migrative t-norms.