Coherent lower probabilities are one of the most general tools within Imprecise Probability Theory, and can be used to model the available information about an unknown or partially known precise probability. In spite of their generality, coherent lower probabilities are sometimes difficult to deal with. For this reason, in previous papers we studied the problem of outer approximating a given coherent lower probability by a more tractable model, such as a 2- or completely monotone lower probability. Unfortunately, such an outer approximation is not unique in general, even if we restrict our attention to those that are undominated by other models from the same family. In this paper, we investigate whether a number of approaches may help in selecting a unique undominated outer approximation. These are based on minimising a distance with respect to the initial model, maximising the specificity, or preserving the same preferences as the original model. We apply them to 2- and completely monotone approximating lower probabilities, and also to the particular cases of possibility measures and p-boxes.

相干较低概率是不精确概率理论中最通用的工具之一，可用于对有关未知或部分已知的精确概率的可用信息进行建模。尽管它们具有普遍性，但有时难以处理相干的较低概率。出于这个原因，在之前的论文中，我们研究了通过更易于处理的模型（例如 2 或完全单调的低概率）外逼近给定的相干低概率的问题。不幸的是，这种外部近似通常并不是唯一的，即使我们将注意力限制在那些不受同一家族其他模型支配的模型上。在本文中，我们研究了多种方法是否有助于选择独特的非支配外部近似。这些基于最小化与初始模型的距离、最大化特异性或保留与原始模型相同的偏好。我们将它们应用于 2- 和完全单调的近似较低概率，以及可能性度量的特殊情况和p盒。