Title
Universal integrals based on copulas
Abstract
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.
Year
DOI
Venue
2014
10.1007/s10700-014-9182-4
Fuzzy Optimization and Decision Making
Keywords
Field
DocType
Capacity,Copula,Universal integral,Choquet integral,Sugeno integral,Shilkret integral
Discrete mathematics,Copula (linguistics),Sugeno integral,Fuzzy logic,Multiplication,Choquet integral,Greatest element,Multiple integral,Mathematics
Journal
Volume
Issue
ISSN
13
3
1568-4539
Citations 
PageRank 
References 
12
1.42
9
Authors
4
Name
Order
Citations
PageRank
Erich Peter Klement1989128.89
Radko Mesiar23778472.41
Fabio Spizzichino38616.34
Andrea StupňAnová411517.40