UNCERTAIN DYNAMICAL-SYSTEMS DEFINED BY PSEUDOMEASURES

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.