FCM is a clustering method which needs cluster number (k) like other non-hierarchical clustering algorithms. But before statrting to clustering process you can estimate the cluster number by using different techniques. Here is a study you can trade on about this topic.

Article Intelligent Choice of the Number of Clusters in K-Means Clus...

On the page bellow you'll find 3 methods with examples.

The elbow method, silhouette and gap statistic.

I've tried them all before with different results. In my opinion, the elbow method, although subjective, is very intuitive. You observe Total Within Sum of Squares decay and decide wether a given number os clusters seems reasonable for you.

https://www.datanovia.com/en/lessons/determining-the-optimal-number-of-clusters-3-must-know-methods/

The same techniques used in other classifier, like k-means, apply here. The number of cluster in an hyper-parameter. So you must use search technique with a validation data to determine the best value.

Seach technique could include:

* Grid search

* Cross validation

*...

Here is an extensive list of those techniques:

https://scikit-learn.org/stable/model_selection.html

I Think this book can help you (p. 481):

Venables, W. N., Ripley, B. D., 2002. Modern applied statistics with 99

S, 4th Edition. Springer-Verlag, New York, p. 481.

For determine the good number of cluster you may use visualisation on our site

https://www.sciencehunter.net/Services/Clustering#/visualization. See video and example - https://www.youtube.com/watch?v=ckTu1fNX5p0&feature=youtu.be