Fuzzy possibilities as upper previsions
In this paper we analyze, mainly in a finitary setting, the consistency properties of fuzzy possibilities, interpreting them as instances of upper previsions and applying the basic notions of avoiding sure loss and coherence from the theory of imprecise probabilities. It ensues that fuzzy possibilities always avoid sure loss, but satisfy the stronger coherence condition only in a special case. Their natural extension, i.e. their least-committal correction to a coherent upper prevision, is determined. The same analysis is then performed when min is replaced in the definition of fuzzy possibility by a T-norm or, more generally, a seminorm, showing that the consistency properties and also the natural extension remain the same. Some "closure" properties are also discussed, which are guaranteed to hold if the T-seminorm is continuous, and are satisfied by (ordinary) possibilities too.
fuzzy possibilities upper previsions imprecise probabilities fuzzy events