On an idempotent transformation of aggregation functions and its application on absolutely continuous Archimedean copulas
In this paper, we isolate an interesting transformation of binary aggregation functions from a result on the propagation of transitivity in additive preference structures. This transformation is based on a projection technique and results in a smaller (or equal) binary aggregation function. The transformation is idempotent and acts internally on the classes of conjunctors, semi-copulas and quasi-copulas. Hence, also copulas are transformed into quasi-copulas, but in general not into copulas. Remarkably, the Frank copulas are mapped to new copulas. (C) 2008 Elsevier B.V. All rights reserved.
archimedean copula copula binary aggregation function transitivity projection conjunctor semi-copula frank copula absolutely continuous copula quasi-copula