Axiomatizations of Lovász extensions of pseudo-Boolean functions

  title={Axiomatizations of Lov{\'a}sz extensions of pseudo-Boolean functions},
  author={Miguel Couceiro and Jean-Luc Marichal},
  journal={Fuzzy Sets and Systems},
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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