On Some Classes of Aggregation Functions that are Migrative

In this paper we introduce and describe two classes of aggregation functions with members that are migrative. First continuous triangular norms are studied that own the migrative property with respect to another fixed t-norm, in particular to the three prototypes minimum, product, and the Łukasiewicz t-norm. For classes of nilpotent and strict migrative t-norms the characterization and construction is carried out by solving functional equations for the generators. For the third case when the fixed t-norm is the minimum, an ordinal-sum-like construction is resulted. Then we formulate and study the migrative property for quasi-arithmetic means. The results are less permissive than for t-norms: we can hardly escape from the classical arithmetic mean. Keywords— Triangular norms, quasi-arithmetic means, functional equations, migrative property.