About this subject, I wrote the following report:
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MODELING WITH UNCERTAINTY IN CONTINUOUS DYNAMICAL
SYSTEMS: THE PROBABILITY AND POSSIBILITY APPROACH
Gianluca Bontempi
(Technical report IRIDIA-ULB-September 95)
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 parameters 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.
Paper available from
ftp iridia.ulb.ac.be (164.15.11.65)
> ftp iridia.ulb.ac.be
Connected to iridia0.ulb.ac.be.
220 iridia0 FTP server (Version wu-2.4(2) Wed Jun 29 20:03:51 MET DST 1994)
ready.
Name : anonymous
331 Guest login ok, send your complete e-mail address as password.
Password:
230 Guest login ok, access restrictions apply.
ftp> cd pub/gbonte/papers
250 CWD command successful.
ftp>bin
200 Type set to I.
ftp> get Tech_report_95.ps.Z
[...]
ftp>bye