Comments on 'a behavioural model for vague probability assessments' (G. de Cooman)

Gert de Cooman has presented a sound and deep approach to vague probability, providing a behavioural interpretation for it. He proposes natural extension as the basic inference procedure, a simple and a general method from which very diverse inference rules can be deduced. This paper discusses some aspects of de Cooman's approach. First, I consider the possibility of extending the approach to general vague magnitudes. Then, I try to put in clear the relationships of vague probability with another approaches as the general theory of imprecise probability and Zadeh's difinition of fuzzy probability. Finally, I give an example of full possibilistic prevision that can be obtained by conditioning a credal set to an observation and propose the use of more general behaviour functions.