**Abstract:** Fuzzy Bayesian networks (FBN) are a model representation for machine learning tachniques. They are graphical structures with variables that are simultaneously fuzzy and uncertain.

Although very similar to classic discrete or multinomial Bayesian networks (BN), and able to take advantage of existing BN techniques and algorithms, belief propagation in a FBN is different and can be too slow on some graphs. Propagating expected values effectively addresses this problem. Because the variables are simultaneously fuzzy and uncertain it can also be confusing. In this paper we summarise fuzzy Bayesian networks and provide examples of forward propagation, backward propagation and explaining away for the same classic BN and FBN.

By comparing, contrasting and interpreting classic BN and FBN side by side, belief propagation in FBN is made clearer, and the strengths of FBN over classic BN in certain situations are also high lighted.

@InProceedings{fogelberg2008h, author = {Christopher Fogelberg}, title = {Belief Propagation in Fuzzy {B}ayesian Networks: A Worked Example}, booktitle = {Proceedings of the 2008 Oxford University Computing Laboratory Student Conference}, year = 2008, editor = {Shamal Faily and Standa Zivny}, month = {October}, keywords = {submitted, fuzzy, bayesian network, fbn, belief propagation, message passing}, url = {http://syntilect.com/cgf/pubs:fbn-example} }

The extended abstract submitted to the conference is available here, and the long version of the paper with the worked examples is available here. Slides are available here, and the 4-up handout is available here. The full conference proceedings are available here.