Discrete Integrals Based on Comonotonic Modularity

@article{Couceiro2013DiscreteIB,
  title={Discrete Integrals Based on Comonotonic Modularity},
  author={Miguel Couceiro and Jean-Luc Marichal},
  journal={Axioms},
  year={2013},
  volume={2},
  pages={390-403}
}
It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals as well as natural extensions of Sugeno integrals. 

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