Discrete integrals based on comonotonic modularity

Abstract

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.

References in corpus (5)

• Polynomial functions over bounded distributive lattices
• Axiomatizations of Lovász extensions of pseudo-Boolean functions
• Quasi-polynomial functions over bounded distributive lattices
• Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions
• Axiomatizations of signed discrete Choquet integrals

Cited by in corpus (1)

• A complete classification of equational classes of threshold functions included in clones