In the previous post we talked about the steps to compute the terms for the cosine distances and the feature/relevance weights in each iteration. This we could do with  the parameters we had during each iteration. We started talking about how to update and adjust the relevance weights. So let's wrap that up and get to computing the weighted aggregated Dwcij and adjusting it if it's negative. So picking up the thread from the relevance weights, we saw that it depends on a default value and a bias. We computed the bias by initializing the fuzzy membership values. Other than the tau, everything else was known to compute the relevance weights. For tau, we wanted to compute it for iteration t with something like the following equation tau-t = K-constant * ((Sum-fuzzy-memberships)(Sum-weighted-cosine))/Sum-relevance-weight-squared) Here we see that we have everything we need to compute for t given K is a constant. So relevance weights can be calculated. we just need initial values for the first iteration and the previous iteration values in the next one.
Now let's look at the weighted aggregated Dwcij and the Dwcij,
 Computing the weighted aggregated Dwcij is know as equal to  Summation over N (vik.Dwcij).
Its the negative values we need to make adjustment on. Here for each of the clusters we compute the absolute value of weighted aggregated Dwcij and take the minimum. This is the adjustment value we add to the weighted aggregated Dwcij that comes out to be minimum.
Note that the previous iteration values of Dwcij are not used in the next iteration but they are recomputed. This is because they are based on cluster centers which we update in each iteration. The adjustment to the negative value for Dwcij follows a similar pattern as adjusting the negative value for relevance weights that we have seen earlier.