n-Monotone exact functionals

TL;DR

This paper explores n-monotone functionals, extending set functions, and establishes a representation theorem linking exact n-monotone functionals to Choquet integrals, advancing theoretical understanding in imprecise probabilities.

Contribution

It introduces new representation results for exact n-monotone functionals using Choquet integrals, improving existing theoretical frameworks.

Findings

Representation of exact n-monotone functionals via Choquet integrals

Enhanced understanding of the relation between n-monotonicity and exactness

Improved theoretical results in imprecise probability theory

Abstract

We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise the notions of coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals.