The variance of the distribution shown, which is from the 500 samples identified, gives us some measure of the probability distribution of that prediction. This in essence indicates that the Bayesian formulation allows us to interpret the predictions of neurorough models in probability terms as can be viewed from a probability distribution. 

![0_image_0.png](0_image_0.png)

## Rule Extraction

Once Bayesian neuro-rough model was applied to the HIV data, unique distinguishable cases and indiscernible cases were extracted. From the data set of 12945 cases, the data is only a representative of 452 cases out of the possible 4096 unique combinations. The lower approximation cases are rules that always hold, or are definite cases while the upper approximation can only be stated with certain plausibility. Examples of both cases that were extracted from the approach in this paper is: If Race = AF and **Mother's Age =** Young and Education = Secondary and Gravidity = Low and Parity = Low and **Father's** 
Age = Young then γ = − 75.0 meaning probably HIV negative. This demonstrates that 