What is Probabilistic (Fuzzy) Clustering?

Probabilistic (Fuzzy) Clustering: Each observation is assigned to one or more clusters with a probability of belonging to each. The cluster assignments are conceptualized as having a probability distribution of belonging to each cluster rather than one exclusive assignment. This has the advantage of quantifying uncertainty if there is ambiguity in cluster assignments. There exists a fuzzy version of K-Means that implements soft clustering, and Expectation-Maximization approaches like Gaussian Mixture models also have this capability.