Aggregation via Clone Theory Approach

Abstract

In our recent papers we have observed that the set of aggregation functions (on any bounded poset) contains all the projections and it is composition-closed. These classes of functions, called clones, are very intensively studied for decades in many different branches of mathematics. The aim of our paper is to give an extended overview of results concerning certain important clones of aggregation functions on bounded lattices. In particular, we focus on the full clone of aggregation functions, the clone of idempotent aggregation functions, the clone of Sugeno integrals and the clone of polynomial functions.