The Gödel integral is a variant of the Sugeno integral. It is an expressive aggregation operator to compute a global evaluation combining local values taken for a set of considered criteria and a capacity, a set function that represents the importance of these criteria and their interactions. A crucial question is then the elicitation of this capacity so as to match the user preferences. Such a task is common in many fields, such as XAI, where counterfactual explanations can be generated in the form of counterfactual examples by aggregating a pair of objective and subjective criteria. In this paper, we focus on approaches to elicit such a capacity when the user preferences are expressed as an ordering relation between classes of equivalent objects. We first propose a theoretical characterisation of the set of admissible capacities: it allows to determine lower and upper bounds of possible capacities when it is not empty and it provides explanations when it is empty. Then, we introduce the algorithm GICEP (for Gödel Integral for Capacity Elicitation from Preference relations), to compute these bounds and to provide explanations. Experiments conducted on synthetic data show the relevance and efficiency of GICEP.