A generalization of the migrativity property of aggregation functions

This paper brings a generalization of the migrativity property of aggregation functions, suggested in earlier work of some of the present authors by imposing the α-migrativity property of Durante and Sarkoci for all values of α instead of a single one. Replacing the algebraic product by an arbitrary aggregation function B naturally leads to the properties of α–B-migrativity and B-migrativity. This generalization establishes a link between migrativity and a particular case of Aczel’s general associativity equation, already considered by Cutello and Montero as a recursive formula for aggregation. Following a basic investigation, emphasis is put on aggregation functions that can be represented in terms of an additive generator, more specifically, strict t-norms, strict t-conorms and representable uninorms.