Smooth aggregation functions on finite scales

Authors:
Margalida Mas;Miquel Monserrat;Joan Torrens
Affiliations:
Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain
Venue:
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Year:
2010

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Abstract

In this paper smooth aggregation functions on a finite scale are studied and characterized as solutions of a functional equation analogous to the Frank functional equation. The particular cases of quasi-copulas and copulas are also characterized through a similar functional equation. Previous characterizations of these kind of operations through special matrices are used jointly with the new ones to derive some invariant properties on quasi-copulas and copulas on finite scales.