whats is the difference between “k means” and “fuzzy c means” objective functions?

Question

I am trying to see if the performance of both can be compared based on the objective functions they work on?

Answer 1

C-means is fuzzy but k-means is hard (is not fuzzy), each point is belonging to a centroid in K-means, but in fuzzy c-means each point can be belonging to two centroids but with different quality.

each point either is a part of the first centroids, or the second centroids.but in C-means, one point can be part of first centroids (90%) and second centroids (10%).for example, student failed or passed if she/he has 49. it somehow is pass and the reality is failed, that time we called fuzzy.