Symmetrization of modular aggregation functions

Authors:
Radko Mesiar;Andrea Mesiarová-Zemánková
Affiliations:
Slovak University of Technology, Bratislava, Slovakia and Institute for Research and Application of Fuzzy Modelling, University of Ostrava, Czech Republic;Mathematical Institute of SAS, Bratislava, Slovakia
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

Ordered modular aggregation functions (OMAF in short) can be seen as symmetrized modular aggregation functions and they are characterized by comonotone modularity. As such, OMAFs generalize OWA operators. We show a one-to-one correspondence between idempotent OMAFs and copula-based integrals with respect to a symmetric capacity.