Working paper
A generalization of the conjunction rule for aggregating contradictory sources of information based on generalized credal sets
In the paper we continue investigations started in the paper presented at ISIPTA’15, where the notions of lower and upper generalized credal sets has been introduced. Generalized credal sets are models of imprecise probabilities, where it is possible to describe contradiction in information, when the avoiding sure loss condition is not satisfied. The paper contains the basic principles of approximate reasoning: models of uncertainty based on upper previsions and generalized credal sets, natural extension, and coherence principles.
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.
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