Data clustering is useful in several areas, such as web mining, biology, climate, medical diagnosis, computer vision, marketing and others. Thus, in real problems, data can simultaneously belong to more than one cluster, being necessary to use fuzzy clustering concepts as decision mechanisms to assign data into clusters. Moreover, nature-based intelligent mechanisms have been used to increase the effectiveness of several machine learning algorithms. This paper proposes improvements on aiNet (Artificial Immune Network), a bioinspired clustering algorithm, and its extension to be applied to fuzzy partitions. The modified algorithm to be applied in fuzzy partitions was thus named FaiNet (Fuzzy aiNet). It uses immune system concepts to allow it to automatically detect a suitable number of clusters in the datasets, what is not possible for most clustering algorithms. FaiNet was applied to seven databases from the literature with the purpose of benchmarking and its performance was compared with that of Fuzzy C-Means, a Fuzzy particle swarm clustering algorithm (FPSC) and the improved crisp aiNet. Purity and Entropy were the main metrics used to evaluate performance. The FaiNet algorithm showed to be competitive with the other algorithms used for comparison.