We investigate the coherence of a possibilistic system modelled by the joint possibility distribution function of a finite sequence of linearly ordered possibilistic variables together with the conditional possibility distribution function of any variable in this sequence, given the values assumed by all preceding variables. To ensure the coherence of this model it is necessary and sufficient that the conditional possibilities are intermediate between those calculated from the joint possibility distribution function by Dempster's rule and the natural extension rule. We then show how a coherent model of conditional and unconditional upper probabilities can be constructed, using a given coherent model and a finitely additive probability. The method used to construct this model is to form convex combinations of the finitely additive probability and the upper probabilities belonging to the given model.
Keywords. Coherence, natural extension rule, Dempster's conditioning rule, possibility measure, upper probability
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