Two views of belief: belief as generalized probability and belief as evidence
Artificial Intelligence
Robust Learning with Missing Data
Machine Learning
Uncertainty-Based Information: Elements of Generalized Information Theory
Uncertainty-Based Information: Elements of Generalized Information Theory
Updating beliefs with incomplete observations
Artificial Intelligence
An introduction to the imprecise Dirichlet model for multinomial data
International Journal of Approximate Reasoning
Decision making under incomplete data using the imprecise Dirichlet model
International Journal of Approximate Reasoning
Second-order uncertainty calculations by using the imprecise Dirichlet model
Intelligent Data Analysis
Modelling Radial Basis Functions with Rational Logic Rules
HAIS '08 Proceedings of the 3rd international workshop on Hybrid Artificial Intelligence Systems
Interpreting Belief Functions as Dirichlet Distributions
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
A new ranking procedure by incomplete pairwise comparisons using preference subsets
Intelligent Data Analysis
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A belief function can be viewed as a generalized probability function and the belief and plausibility measures can be regarded as lower and upper bounds for the probability of an event. However, the classical probabilistic interpretation used for computing belief and plausibility measures may be unreasonable in many real applications when the number of observations or measurements is rather small. In order to overcome this difficulty, Walley's imprecise Dirichlet model is used to extend the belief, plausibility and possibility measures. An interesting relationship between belief measures and sets of multinomial models is established. Combination rules taking into account reliability of sources of data are studied. Various numerical examples illustrate the proposed extension.