Fuzzy clustering is still a thriving issue as can witness the wealthy number of related work. Thus, a data point can simultaneously belong to several clusters, with different degrees of membership, i. e., objects on the boundaries between several clusters have gradual membership degrees. Within the scrutinised related work, the main focus was paid to the automatic determination of the number of clusters. In this paper, we introduce a new algorithm, called Fuzzy-MSOM, of unsupervised fuzzy clustering. The clustering process is carried out through a multi-level approach, where the data is first clustered using a fuzzy neural network clustering algorithm, called FSOM, and then the output is iteratively clustered. To do so, the introduced approach heavily relies on a defuzzification process. The quality assessment of the each cluster is done through the Partition Coefficient and Exponential Separation index. The extensive carried out experiments stress on the benefits of the introduced approach and show that it outperforms the pioneering approaches of the literature.