Coherent Models for Discrete Possibilistic Systems

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. Possi...

• Type: Conference
• Year: 1999
• Where: ISIPTA
• Authors: Hugo J. Janssen, Gert De Cooman, Etienne E. Kerre
• Keywords: Initial Possibilities, ISIPTA 1999, Markov Condition, Mathematics, One-step Transition Possibilities