2-Increasing binary aggregation operators

In this work we investigate the class of binary aggregation operators (=agops) satisfying the 2-increasing property, obtaining some characterizations for agops having other special properties (e.g., quasi-arithmetic mean, Choquet-integral based, modularity) and presenting some construction methods. In particular, the notion of P-increasing function is used in order to characterize the composition of 2-increasing agops. The lattice structure (with respect to the pointwise order) of some subclasses of 2-increasing agops is presented. Finally, a method is given for constructing copulas beginning from 2-increasing and 1-Lipschitz agops.