Universal integrals based on copulas

0432228 - ÚTIA 2015 RIV US eng J - Journal Article
Klement, E.P. - Mesiar, Radko - Spizzichino, F. - Stupňanová, A.
Universal integrals based on copulas.
Fuzzy Optimization and Decision Making. Roč. 13, č. 3 (2014), s. 273-286. ISSN 1568-4539. E-ISSN 1573-2908
R&D Projects: GA ČR GAP402/11/0378
Institutional support: RVO:67985556
Keywords : capacity * copula * universal integral
Subject RIV: BA - General Mathematics
Impact factor: 2.163, year: 2014
http://library.utia.cas.cz/separaty/2014/E/mesiar-0432228.pdf

A hierarchical family of integrals based on a fixed copula is introduced and discussed. The extremal members of this family correspond to the inner and outer extension of integrals of basic functions, the copula under consideration being the corresponding multiplication. The limits of the members of the family are just copula-based universal integrals as recently introduced in Klement et al. (IEEE Trans Fuzzy Syst 18:178–187, 2010). For the product copula, the family of integrals considered here contains the Choquet and the Shilkret integral, and it belongs to the class of decomposition integrals proposed in Even and Lehrer (Econ Theory, 2013) as well as to the class of superdecomposition integrals introduced in Mesiar et al. (Superdecomposition integral, 2013). For the upper Fréchet-Hoeffding bound, the corresponding hierarchical family contains only two elements: all but the greatest element coincide with the Sugeno integral.
Permanent Link: http://hdl.handle.net/11104/0237118