Aggregation functions given by polynomial functions

In this paper aggregation functions whose expressions are given by polynomial functions are investigated. A detailed study focused on binary polynomial aggregation functions of degree one and two is given not only in general, but also requiring some additional properties like idempotency, commutativity, associativity, one-side neutral (or absorbing) element and so on, leading to some families of binary polynomial aggregation functions. The results concerning polynomials of degree one are generalized to n-ary polynomial aggregation functions whereas, with respect to those of degree two, the commutative case is also generalized obtaining the characterization of all commutative n-ary polynomial aggregation functions of degree two in general and jointly with the idempotent property.