  One way to make decisions under uncertainty is to select an optimal option
from a possible range of options, by maximizing the expected utilities derived
from a probability model. However, under severe uncertainty, identifying
precise probabilities is hard. For this reason, imprecise probability models
uncertainty through convex sets of probabilities, and considers decision rules
that can return multiple options to reflect insufficient information. Many
well-founded decision rules have been studied in the past, but none of those
standard rules are able to control the number of returned alternatives. This
can be a problem for large decision problems, due to the cognitive burden
decision makers have to face when presented with a large number of
alternatives. Our contribution proposes regret-based ideas to construct new
decision rules which return a bounded number of options, where the limit on the
number of options is set in advance by the decision maker as an expression of
their cognitive limitation. We also study their consistency and numerical
behaviour.
