Fuzzy membership and defuzzification

Dear all,

I know this question might be better placed at a statistics forum. Still, since I am used to code in Matlab I thought I first try it here.

I have a matrix P with N rows (objects) and C cols (classes) where each element refers to the probability, that the object n belongs to class c. Now, based on this information, I like to find out the expected value of number of objects in each class as well as its confidence intervals. The expected value m_c might be obtained by simply finding the maximum along each row such that.

B = false(size(P));
[~,ix] = max(P,[],2);
B(sub2ind(size(P),1:size(P,1),ix)) = true;
m_c = sum(B,1);

However, does anyone have an idea how I could calculate the confidence intervals of m_c? I would like to come towards a result that tells me that the expected number of objects in class c is m_c +/- x?

Help is greatly appreciated! Cheers, Anon