This page collects together all of our research on fuzzy Bayesian networks (FBN). A FBN is a Bayesian network that has fuzzy variables, and so it is simultaneously fuzzy and uncertain.
An example of fuzzy uncertainty is the variable R, the probability that it will rain today. In a classic BN the variable R might have an uncertain state. There could be a 0.3 probability that it will not rain at all today, a 0.4 probability that it will rain lightly, and a 0.3 probability that it will rain heavily - i.e. {none0.3, light0.4, heavy0.3}.
However, if R is a variable in a FBN then there might be a 0.3 probability that it will not rain at all for 1/3 of the day, a 0.4 probability that it will rain lightly for 1/3 of the day, and a 0.3 probability that it will rain heavily for 1/3 of the day. For the other 2/3 of the day there could be a 0.7/0.2/0.1 distribution over the chances of none, light and heavy rain. We can denote this as follows:
In general, a fuzzy uncertain variable representation can be used to express more complex information. In addition, the other advantages of fuzziness and Bayesian networks can be used in FBN, and all existing BN algorithms and techniques (such as junction-tree and structural EM) can be used with only minor modification. Further, depending on the approximation to full general FBN belief propagation that is used, FBN inference and propagation may be only a small linear factor less efficient than classic BN. Like BN, FBN are a general machine learning formalisation, and sub-types such as fuzzy HMM and fuzzy Kalman filters can be easily defined.
We've only just begun, so this page is pretty spartan for now. But more is to come!
To familiarise yourself with FBN we suggest reading the first three papers. The slides from the OMI presentation focus on the relationship between fuzziness and uncertainty, and also considers how FBN could be applied.