Practical implementation of possibilistic probability mass functions

Probability assessments of events are often linguistic in nature. We model them by means of possibilistic probabilities (a version of Zadeh’s fuzzy probabilities with a behavioural interpretation) with a suitable shape for practical implementation (on a computer). Employing the tools of interval analysis and the theory of imprecise probabilities we argue that the verification of coherence for these possibilistic probabilities, the corrections of non-coherent to coherent possibilistic probabilities and their extension to other events and gambles can be performed by finite and exact algorithms. The model can furthermore be transformed into an imprecise first-order model, useful for decision making and statistical inference.