Belief propagation in fuzzy Bayesian networks

Fuzzy Bayesian networks are a generalisation of classic Bayesian networks to networks with fuzzy variable state. This paper describes our formalisation and outlines how belief propagation can be conducted. Fuzzy techniques can lead to more robust inference. A key advantage of our formalisation is that it can take advantage of all existing network inference and Bayesian network algorithms. Another key advantage is that we have developed several techniques to control the algorithmic complexity. When these techniques can be applied it means that fuzzy Bayesian networks are only a small linear factor less efficient than classic Bayesian networks. With appropriate pre-processing they may be substantially more efficient.