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 T 0 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 T 0 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.