Discrete integrals based on comonotonic modularity

TL;DR

This paper characterizes and extends classes of discrete integrals, such as Choquet and Sugeno integrals, by exploring their property of comonotonic modularity, leading to broader families including signed variants.

Contribution

It provides an axiomatic framework that identifies new families of comonotonically modular discrete integrals beyond classical types.

Findings

Identifies broader classes of comonotonically modular integrals

Includes signed and symmetric signed Choquet integrals

Extends Sugeno integrals within a unified framework

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.