What is the difference between the words allocation, assignment, affiliation?

What is the difference between the words allocation, assignment, affiliation – or the verbs to allocate, to assign, to affiliate?

I would like to know in general, because I would like to finally understand the difference in general. However, there is an reason that made me realize that I do not know the difference:

The context is fuzzy clustering: I am having objects (which are literally not further specified) which I group into so called clusters. The result is that each object is assinged/allocated/affiliated to each cluster with a certain percentage to each cluster. I don’t know what I am implicated by using either of those words.