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Universal integrals based on copulas
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SYSNO ASEP 0432228 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Universal integrals based on copulas Author(s) Klement, E.P. (AT)
Mesiar, Radko (UTIA-B) RID, ORCID
Spizzichino, F. (IT)
Stupňanová, A. (SK)Number of authors 4 Source Title Fuzzy Optimization and Decision Making - ISSN 1568-4539
Roč. 13, č. 3 (2014), s. 273-286Number of pages 14 s. Publication form Print - P Language eng - English Country US - United States Keywords capacity ; copula ; universal integral Subject RIV BA - General Mathematics R&D Projects GAP402/11/0378 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000339889600002 DOI 10.1007/s10700-014-9182-4 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2015
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