Measures of uncertainty in expert systems
Artificial Intelligence
Notes on conditional previsions
International Journal of Approximate Reasoning
A survey of the theory of coherent lower previsions
International Journal of Approximate Reasoning
Fuzzy Sets and Systems
Unifying practical uncertainty representations -- I: Generalized p-boxes
International Journal of Approximate Reasoning
Probability boxes on totally preordered spaces for multivariate modelling
International Journal of Approximate Reasoning
Independence and 2-monotonicity: nice to have, hard to keep
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
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In imprecise probability theories, independence modeling and computational tractability are two important issues. The former is essential to work with multiple variables and multivariate spaces, while the latter is essential in practical applications. When using lower probabilities to model uncertainty about the value assumed by a variable, satisfying the property of 2-monotonicity decreases the computational burden of inference, hence answering the latter issue. In a first part, this paper investigates whether the joint uncertainty obtained by main existing notions of independence preserve the 2-monotonicity of marginal models. It is shown that it is usually not the case, except for the formal extension of random set independence to 2-monotone lower probabilities. The second part of the paper explores the properties and interests of this extension within the setting of lower probabilities.