Bimigrativity of binary aggregation functions

We introduce the notions of bimigrativity and total bimigrativity of an aggregation function w.r.t. another aggregation function, as a natural generalization of the notions of migrativity and bisymmetry. We investigate the role of the presence of neutral or absorbing elements. We also pay attention to the class of weighted quasi-arithmetic means, a well-known class of bisymmetric aggregation functions.