Friday, 10th September, 2021 11:00 CEST HCAI Research Seminar
Title: Choquet integrals for explainable AI (xAI) – motivation, definition, properties and outlook
Speaker: Prof. Dr. Zdenko TAKAC, Head of the Department of Mathematics, Slovak Technical University in Bratislava (SK)
Abstract:
A Choquet integral [1] is a subadditive or superadditive integral created by the French mathematician Gustave CHOQUET in 1953. It was initially used in statistical mechanics and potential theory, but found its way into decision theory in the 1980s, where it is used as a way of measuring the expected utility of an uncertain event.
The problem of finding an appropriate model of aggregation is crucial in many fields, in particular in multicriteria decision making. It is desirable to handle aggregated data properly, but with a model which is as simple as possible. One of the simplest models of aggregation on the unit hypercube [0,1]^n is an additive aggregation function. Unfortunately, additive aggregation functions are insufficient to model even quite simple preferences, although some of these situations can be treated with the Choquet integrals.
The Choquet integral can be regarded as a generalization of additive aggregation functions replacing the requirement of additivity by that of comonotone additivity. The crucial role in definition of Choquet integral plays fuzzy measure, which is (possibly) a non-additive measure. The use of fuzzy measure allows the Choquet Integral to assign importance to all possible groups of criteria, and thus offers a much greater flexibility for aggregation.
Bio: Zdenko TAKAC is currently an Associate Professor and the Head of the Department of Mathematics, Slovak University of Technology in Bratislava, Slovakia. His research interests include uncertainty modeling, fuzzy sets and fuzzy logic, aggregation operators, interval-valued fuzzy sets and type-2 fuzzy sets. Recently he got interested in the field of explainable AI (XAI).
[1] https://www.sciencedirect.com/topics/mathematics/choquet-integral
