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Journal Article: BibTeX citation key:  Dubois1997
Dubois, D., & Prade, H. (1997). Bayesian conditioning in possibility theory. Fuzzy Sets and Systems, 92(2), 223–240.
Added by: Arnaud Martin 2010-12-19 14:22:24
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Categories: General
Creators: Dubois, Prade
Collection: Fuzzy Sets and Systems

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Abstract
In this paper, possibility measures are viewed as upper bounds of ill-known probabilities, since a possibility distribution is a faithful encoding of a set of lower bounds of probabilities bearing on a nested collection of subsets. Two kinds of conditioning can be envisaged in this framework, namely revision and focusing. On the one hand, revision by a sure event corresponds to adding an extra constraint enforcing that this event is impossible. On the other hand, focusing amounts to a sensitivity analysis on the conditioned probability measures (induced by the lower bound constraints). When focusing on a particular situation, the generic knowledge encoded by the probability bounds is applied to this situation, without aiming at modifying the generic knowledge. It contrasts with revision where the generic knowledge is modified by the new constraint. This paper proves that focusing applied to a possibility measure yields a possibility measure again, which means that the conditioning of a family of probabilities, induced by lower bounds bearing on probabilities of nested events, can be faithfully handled on the possibility representation itself. Relationships with similar results in the belief function setting are pointed out. Lastly the application of possibilistic focusing to exception-tolerant inference is suggested.
Added by: Arnaud Martin