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.

翻译：在不确定性下做出决策的一种方式是从可能的选择范围内通过最大化基于概率模型的期望效用选择最优选项。然而，在强不确定性下，精确概率难以确定。因此，非精确概率通过凸概率集对不确定性建模，并采用可能返回多个选项以反映信息不足的决策规则。以往已研究了许多有充分依据的决策规则，但这些标准规则均无法控制返回备选方案的数量。对于大规模决策问题，由于决策者在面对大量备选方案时必须承受认知负担，这可能成为问题。我们的贡献在于提出基于遗憾的思想，构建能返回有界数量选项的新型决策规则，其中选项数量上限由决策者预先设定，作为其认知限制的体现。我们还研究了这些规则的一致性与数值行为。