Modeling with uncertainty in continuous dynamical systems: the probability and possibility approach

This paper presents probability and possibility as two measures to model different types of uncertainty in continuous dynamical systems. We analyze and compare how probability and possibility distribution evolve in a dynamical system modeled by differential equations, where initial conditions and/or parameter may be uncertain. Moreover, we propose a new algorithm for the numerical resolution of a fuzzy differential system and we relate it to existing computational methods to solve regular stochastic differential equations. Finally, we compare results obtained by simulating a dynamical system in which uncertainty is first represented in a possibilistic and then in a probabilistic form.