point can have membership to multiple clusters. By relaxing the definition of membership coefficients from strictly 1 or 0, these values can range from any value from 1 to 0. The following image shows the data set from the previous clustering, but now fuzzy c-means clustering is applied. First, a new threshold value defining two clusters may be generated. Next, new membership coefficients for each data point are generated based on clusters centroids, as well as distance from each cluster centroid. As one can see, the middle data point belongs to cluster A and cluster B. the value of 0.3 is this data point's membership coefficient for cluster A . Applications Clustering problems have applications in surface science, biology, medicine, psychology, economics, and many other disciplines. Bioinformatics In the field of bioinformatics, clustering is used for a number of applications. One use is as a pattern recognition technique to analyze gene expression data from RNA-sequencing data or other technologies. In this case, genes with similar expression patterns are grouped into the same cluster, and different clusters display distinct, well-separated patterns of expression. Use of clustering can provide insight into gene function and regulation. Because fuzzy clustering allows genes to belong to more than one cluster, it allows for the identification of genes that are conditionally co-regulated or co-expressed. For example, one gene may be acted on by more than one transcription factor, and one gene may encode a protein that has more than one function. Thus, fuzzy clustering is more appropriate than hard clustering. Image analysis Fuzzy c-means has been a very important tool for image processing in clustering objects in an image. In the 1970s, mathematicians introduced the spatial term into the FCM algorithm to improve the accuracy of clustering under noise. Furthermore, FCM algorithms have been used to distinguish between different activities using image-based features such as the Hu and the Zernike Moments. Alternatively, A fuzzy logic model can be described on fuzzy sets that are defined on three components of the HSL color space HSL and HSV; The membership functions aim to describe colors follow the human intuition of color identification. Marketing In marketing, customers can be grouped into fuzzy clusters based on their needs, brand choices, psycho-graphic profiles, or other marketing related partitions. Image processing example Image segmentation using k-means clustering algorithms has long been used for pattern recognition, object detection, and medical imaging. However, due