Universal integrals based on copulas View Full Text


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Article Info

DATE

2014-09

AUTHORS

Erich Peter Klement, Radko Mesiar, Fabio Spizzichino, Andrea Stupňanová

ABSTRACT

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. More... »

PAGES

273-286

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URI

http://scigraph.springernature.com/pub.10.1007/s10700-014-9182-4

DOI

http://dx.doi.org/10.1007/s10700-014-9182-4

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https://app.dimensions.ai/details/publication/pub.1032650967


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143 schema:name Department of Mathematics, University of Rome “La Sapienza”, Rome, Italy
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145 https://www.grid.ac/institutes/grid.9970.7 schema:alternateName Johannes Kepler University of Linz
146 schema:name Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria
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