Conditional Aggregation-Based Choquet Integral as a Choquet Integral on a Hyperspace

TL;DR

This paper demonstrates how the conditional aggregation-based Choquet integral can be represented as a standard Choquet integral on a hyperspace, enabling new insights and computational formulas for this mathematical construct.

Contribution

It provides a novel representation of the conditional aggregation-based Choquet integral as a standard Choquet integral on a hyperset, expanding theoretical understanding and computational methods.

Findings

Derived formulas for computing the conditional aggregation-based Choquet integral.

Established its representation as a Choquet integral on a hyperspace.

Expressed the integral in terms of the Möbius transform.

Abstract

We aim at representing the recently introduced conditional aggregation-based Choquet integral as a standard Choquet integral on a hyperset. The representation is one of transformations considered by R.R. Yager and R. Mesiar in 2015. Thus we study the properties of the conditional aggregation-based Choquet integral using well-known facts about the standard Choquet integral. In particular, we obtain several formulas for its computation. We also provide the representation of the conditional aggregation-based Choquet integral in terms of the M\"obius transform.