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.

Keywords

• aggregation function
• discrete Choquet integral
• discrete Sugeno integral
• functional equation
• comonotonic additivity
• comonotonic modularity
• axiomatization