Possibility theory is a computationally efficient framework for reasoning with imprecise probabilities. Before performing any possibilistic analysis, however, the (imprecise) probabilistic information about the experiment needs to be expressed in the form of a possibility distribution. In this paper, we propose a novel Imprecise Probability-to-Possibility Transformation. This method unifies many results in quantitative possibility theory concerning information modeling, data analysis, and the construction of joint distributions. Furthermore, we show how it enables new results about possibilistic information aggregation and how it may refine frequentist inference in (im-)precise statistical models. The approach is characterized by a clear distinction between the elementary events' well-known objective possibilities from quantitative possibility theory and the elementary events' subjective plausibilities, a reimagination of qualitative possibility measures, which helps overcome several non-uniqueness issues.

可能性理论是一种计算效率高的框架，用于概率不精确的推理。但是，在执行任何可能的分析之前，需要以可能性分布的形式表示有关实验的（不精确的）概率信息。在本文中，我们提出了一种新的不精确概率到可能性的转换。这种方法将有关信息建模，数据分析和联合分布构造的定量可能性理论中的许多结果统一起来。此外，我们展示了它如何实现关于可能性信息聚合的新结果，以及如何在（精确）精确的统计模型中完善频繁推断。该方法的特点是基本事件之间的明显区别