This paper deals with uncertain dynamical systems in which predictions
about the future state of a system are assessed by so-called pseudome
asures. Two special cases are stochastic dynamical systems, where the
pseudomeasure is the conventional probability measure, and fuzzy dynam
ical systems in which the pseudomeasure is a so-called possibility mea
sure. New results about possibilistic systems and their relation to de
terministic and to stochastic systems are derived by using idempotent
pseudolinear algebra. By expressing large deviation estimates for stoc
hastic perturbations in terms of possibility measures, we obtain a new
interpretation of the Freidlin-Wentzell quasipotentials for stochasti
c perturbations of dynamical systems as invariant possibility densitie
s. (C) 1997 American Institute of Physics.