Elicitation and Preference relations with Godel integral

To express user’s preferences is a complex task but usually necessary in various domains such as, for instance, eXplainable AI (XAI) when generating counterfactual explanations that combine an objective quality criterion and a subjective criterion related to the user’s knowledge. In this paper, we introduce a G¨odel integral to aggregate these criteria and we propose a new approach to elicit the capacity, parameter of this integral, with the use of the user’s preferences expressed as an order relation between classes of objects. After a theoretical characterization of the set of admissible solutions for this problem, we propose the GICEP algorithm to determine these solutions or provide the user with explanations if no capacity can be found to model their preferences. Experiments carried out on synthetic data highlight the relevance and effectiveness of this approach.