The binomial decomposition of OWA functions, the 2-additive and 3-additive cases in n dimensions

In the context of the binomial decomposition of OWA functions, we investigate the constraints associated with the 2-additive and 3-additive cases in n dimensions. The 2-additive case depends on one coefficient whose feasible region does not depend on the dimension n. On the other hand, the feasible region of the 3-additive case depends on two coefficients and is explicitly dependent on the dimension n. This feasible region is a convex polygon with n vertices and n edges, which is strictly expanding in the dimension n. The orness of the OWA functions within the feasible region is linear in the two coefficients, and the vertices associated with maximum and minimum orness are identied. Finally, we discuss the 3-additive binomial de-composition in the asymptotic innite dimensional limit.