Modelling uncertainty with generalized credal sets: application to conjunction and decision.
To model conflict, non-specificity and contradiction in information,
upper and lower generalized credal sets are introduced. Any upper
generalized credal set is a convex subset of plausibility measures
interpreted as lower probabilities whose bodies of evidence consist of
singletons and a certain event. Analogously, contradiction is modelled
in the theory of evidence by a belief function that is greater than
zero at empty set. Based on generalized credal sets, we extend the
conjunctive rule for contradictory sources of information, introduce
constructions like natural extension in the theory of imprecise
probabilities and show that the model of generalized credal sets
coincides with the model of imprecise probabilities if the profile of
a generalized credal set consists of probability measures. We give
ways how the introduced model can be applied to decision problems.