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Fuzzy clustering is an alternative method to conventional or hard clustering algorithms, which makes partitions of data containing similar subjects. The tendency of adopting machine learning, big data science, cloud computation in various industries depends on unsupervised learning on data structures to tell the story about consumers' behavior, fraud detection, and market segmentation. Fuzzy clustering contrasts with hard clustering by its nonlinear nature and discipline of flexibility in grouping massive data. It provides more accurate and close-to-nature solutions for partitions and herein implies more possibility of solutions for decision-making. In the specific matter of computation, fuzzy clustering has its roots in fuzzy logic and indicates the likelihood or degrees of one data point belonging to more than one group. This paper focuses on the study of models of fuzzy clustering in various cases. Uniquely designed algorithms enhance the accuracy of outcomes and are worth studying to assist future work. In some case scenarios, modeling processes are data-driven and place emphasis on the distances between points and new centers of clusters. In some other cases, which aim at market segmentation or evaluation of patients by healthcare records, membership degree is a key element in the algorithm. This paper surveys a wide-range of research that has well-designed mathematic models for fuzzy clustering, some of which include genetic algorithms and neural networks. The last section introduces open sources of Python and displays sample results from hands-on practice with these packages.