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Universal integrals based on copulas
No full textA 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. © 2014 Springer Science+Business Media New York.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, Mesiar & Pap, IEEE Trans. Fuzzy Systems, 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 & Lehrer, Economic Theory, 2013] as well as to the class of superdecomposition integrals introduced by Mesiar, Li & Pap. For the upper Frechet-Hoeffding bound, the corresponding hierarchical family contains only two elements: all but the greatest element coincide with the Sugeno integral
Special Issue on Set Valued Analysis 2021
No full textSet Valued Analysis plays an important role in the study of statistics, biology, economics, social sciences, optimal control, differential inclusions, image reconstruction and fixed point theory [...
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