Some Remarks About Polynomial Aggregation Functions

There exist a great quantity of aggregation functions at disposal to be used in different applications. The choice of one of them over the others in each case depends on many factors. In particular, in order to have an easier implementation, the selected aggregation is required to have an expression as simple as possible. In this line, aggregation functions given by polynomial expressions were investigated in [22]. In this paper we continue this investigation focussing on binary aggregation functions given by polynomial expressions only in a particular sub-domain of the unit square. Specifically, splitting the unit square by using the classical negation, the aggregation function is given by a polynomial of degree one or two in one of the sub-domains and by 0 (or 1) in the other sub-domain. This is done not only in general, but also requiring some additional properties like idempotency, commutativity, associativity, neutral (or absorbing) element and so on, leading to some families of binary polynomial aggregation functions with a non-trivial 0 (or 1) region.