####
FIRST INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

####
Ghent, Belgium

30 June - 2 July 1999

##
** ELECTRONIC PROCEEDINGS **

## Hugo J. Janssen, Gert de Cooman, and Etienne E. Kerre

# Coherent Models for Discrete Possibilistic Systems

** Abstract **

We consider discrete possibilistic systems for which the available
information is given by one-step transition possibilities and initial
possibilities. These systems can be represented by a collection of
variables satisfying a possibilistic counterpart of the Markov
condition. This means that, given the values assumed by a selection of
variables, the possibility that a subsequent variable assumes some
value is only dependent on the value taken by the most recent variable
of the selection. The one-step transition possibilities are recovered
by computing the conditional possibility of any two consecutive
variables. Under the behavioural interpretation as marginal betting
rates against events these 'conditional' possibilities and the
initial possibilities should satisfy the rationality criteria of
'avoiding sure loss' and 'coherence'. We show that this is indeed
the case when the conditional possibilities are defined using
Dempster's conditioning rule.

** Keywords. ** Possibilistic Markov system, Markov condition, coherence, Dempster's conditioning rule.

The paper is available in the following formats:

** Authors addresses: ** Hugo J. Janssen

Universiteit Gent

Krijgslaan 281--S9

9000 Gent, Belgium

Gert de Cooman

Universiteit Gent

Technologiepark -- Zwijnaarde 9

9052 Zwijnaarde, Belgium

Etienne E. Kerre

Universiteit Gent

Krijgslaan 281--S9

9000 Gent, Belgium

** E-mail addresses: **

[ back
to the Proceedings of ISIPTA '99 home page ]

Send any remarks to the following address:
smc@decsai.ugr.es