Robust Integrals

TL;DR

This paper introduces robust versions of the Choquet, Shilkret, and Sugeno integrals for decision analysis, capable of aggregating interval evaluations, and provides axiomatic foundations for the robust Choquet integral.

Contribution

It generalizes existing integrals to handle interval evaluations and offers an axiomatic characterization of the robust Choquet integral.

Findings

Robust integrals reduce to classical integrals when evaluations are exact.

Robust integrals effectively aggregate interval-based evaluations.

Axiomatic foundation established for the robust Choquet integral.

Abstract

In decision analysis and especially in multiple criteria decision analysis, several non additive integrals have been introduced in the last years. Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno integral. In the context of multiple criteria decision analysis, these integrals are used to aggregate the evaluations of possible choice alternatives, with respect to several criteria, into a single overall evaluation. These integrals request the starting evaluations to be expressed in terms of exact-evaluations. In this paper we present the robust Choquet, Shilkret and Sugeno integrals, computed with respect to an interval capacity. These are quite natural generalizations of the Choquet, Shilkret and Sugeno integrals, useful to aggregate interval-evaluations of choice alternatives into a single overall evaluation. We show that, when the interval-evaluations collapse into exact-evaluations, our definitions of robust integrals collapse into the previous definitions. We also provide an axiomatic characterization of the robust Choquet integral.