By now i thought that fuzzy clustering can be applied to any kind of data-sets but now i have heard that it can be applied only to specific data-sets that involve the concept of probability, is that true?


First I would say the fuzzy clustering is not necessarily a clustering algorithm which uses fuzzy logic.

In machine learning terminology, a "soft" clustering algorithm is called fuzzy clustering as the intuition behind it is not "crisp" (like hard clustering algorithms in which a data point belongs ONLY to one cluster and not others) i.e. for each data point, they output a vector of "probabilities" corresponding to the membership of that point to each cluster (please note that fuzzy memberships are not necessarily probabilities). Even in FCM algorithm, you are just doing a soft version of k-means and it has nothing to do with fuzzy logic (except of the very general idea i.e. not being crisp in making decision)

So you can apply them to any dataset.

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