On an idempotent transformation of aggregation functions and its application on absolutely continuous Archimedean copulas

Authors:
B. De Baets;H. De Meyer;S. Díaz
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium;Department of Statistics and O.R., Faculty of Science, University of Oviedo, Calvo Sotelo s/n, 33007 Oviedo, Spain
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

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.