Probabilistic-Possibilistic Belief Networks
Abstract
This paper introduces probabilistic-possibilistic belief networks as a framework for modeling uncertain knowledge by combining probability theory and possibility theory. Membership functions of fuzzy sets are interpreted as likelihood functions, enabling a hierarchical representation of uncertainty that integrates both stochastic and epistemic components.
The approach extends Bayesian and credal networks by incorporating fuzzy probabilities, allowing for more flexible modeling of imprecision while fully utilizing available data. The study also examines updating mechanisms, highlighting the advantages over traditional imprecise probability methods, and demonstrates how graphical structures such as belief networks can support efficient inference through d-separation.
The results show that probabilistic-possibilistic models provide a richer and more consistent framework for decision-making under uncertainty.
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