Fuzzy C-Means (FCM) is an unsupervised clustering algorithm that allows data points to belong to multiple clusters with varying degrees of membership. Unlike traditional hard clustering methods, where each data point is assigned to a single cluster, FCM assigns a probability score to each data point for each cluster, indicating the likelihood of its membership. This approach is particularly useful for datasets where points may naturally belong to more than one category.

The algorithm operates by initializing cluster centers and a partition matrix that represents the degree of membership of each data point to each cluster. It iteratively updates the cluster centers and the partition matrix until convergence is achieved. The key parameters in FCM include the membership value (μ_ij), which indicates the probability of a data point belonging to a cluster, and the fuzzifier (m), which controls the level of fuzziness in the clustering process ²⁴.

FCM is advantageous in scenarios with overlapping data, as it provides a more nuanced understanding of data relationships compared to hard clustering methods like K-Means ⁴.