  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.
