When it comes to explainable prediction, there is great potential for modeling data with high accuracy and flexibility using fuzzy integrals such as the Choquet integral. In this contribution, we investigate the trade-off between flexibility and tractability when learning fuzzy measures, and propose a method involving random subset selection for reducing the size of the fitting problem when datasets are too large for learning a general fuzzy measure. We conduct some numerical experiments to compare some existing simplification approaches and show that random subset selection, especially when based on partitions, could serve as a suitable compromise if we want to incorporate interaction between larger subsets. We note the savings in both the number of variables and number of constraints required depending on how the random subsets are chosen.