Does the Membership Matrix of Fuzzy C-Means Clustering contain probabilities or degrees of membership?

Question

I recently heard a lecture on Fuzzy C-Means Clustering that stated that the Membership Matrix contains probabilities that particular data points are members of particular clusters. I was confused by this because in "standard" Fuzzy Logic, degree of membership is not the same thing as probability of membership; for example, a value of 0.1 would indicate that the item in question is 10% a member of a particular set, not that there's a 10% probability of it being a member of a set.

Can someone explain what the Membership Matrix? Is it probabilities or degrees of membership and why?

Answer 1

The membership function, $u_{ik}$, is a probability that object $i$ is a member of cluster $k$, with range [0,1].