A universal approach to imprecise probabilities in possibility theory

Abstract 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.