Axiomatizations of Lovász extensions of pseudo-Boolean functions

@article{Couceiro2011AxiomatizationsOL,
  title={Axiomatizations of Lov{\'a}sz extensions of pseudo-Boolean functions},
  author={Miguel Couceiro and Jean-Luc Marichal},
  journal={Fuzzy Sets and Systems},
  year={2011},
  volume={181},
  pages={28-38}
}
Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity conditions, these functions coincide with the Lovász extensions vanishing at the origin, which subsume the… CONTINUE READING
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References

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Integral with respect to a pre-measure

J. Šipoš
Mathematica Slovaca, • 1979
View 4 Excerpts
Highly Influenced

Aggregation functions. Encyclopedia of Mathematics and its Applications 127

M. Grabisch, J.-L. Marichal, R. Mesiar, E. Pap
2009

An introduction to the theory of functional equations and inequalities: Cauchy’s equation and Jensen’s inequality

M. Kuczma
Birkhäuser, Basel, • 2008

Aggregation Functions: A Guide for Practitioners

Studies in Fuzziness and Soft Computing • 2007
View 1 Excerpt

Monotone set functions-based integrals

P. Benvenuti, R. Mesiar, D. Vivona
In Handbook of measure theory, • 2002

Fuzzy measures and integrals - Theory and applications, volume 40 of Studies in Fuzziness and Soft Computing

M. Grabisch, T. Murofushi, M. Sugeno, editors
2000
View 1 Excerpt

Functional equations in several variables

J. Aczél, J. Dhombres
Encyclopedia of Mathematics and its Applications • 1989

Extensions of functions of 0-1 variables and applications to combinatorial optimization

I. Singer
Numer. Funct. Anal. Optimization, • 1984
View 1 Excerpt

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