I am trying to implement C4.5 and I use Quinlan's book called also "C4.5: Programs for Machine Learning". The pruning method proposed by C4.5 is to use a pessimistic CI-based estimate of the error from a node. So, given a confidence level ($\alpha$), the total weight of the cases considered $N$, and the total weight of the mis-classified cases $E$, the proposed estimator is the upper limit of the confidence interval for binomial distribution with $N$ trials and $E$ errors.
I fully understand that we are not talking here about a sample, that the estimated value is more or less a heuristic, and so on. I am not interested in this, I try to met all the original specifications.
The problem which I do not understand is the following one: due to how the missing values are handled by C4.5, it is usual to have quantities $N$ and $E$ as non-integer values. If this is the case, how can one compute CI for binomial?
Note: Now I am currently studying this article: http://www.sigmazone.com/binomial_confidence_interval.htm to give me some light on this topic. Still, I believe that this will not solve my problem.