The term “big data” means a large amount of data, and big data management refers to the efficient handling, organization, or use of large volumes of structured and unstructured data belonging to an organization. Due to the gradual availability of plenty of raw data, the knowledge extraction process from big data is a very difficult task for most of the classical data mining and machine learning tools. In a previous paper, the correlative naive Bayes (CNB) classifier was developed for big data classification. This work incorporates the fuzzy theory along with the CNB classifier to develop the fuzzy CNB (FCNB) classifier. The proposed FCNB classifier solves the big data classification problem by using the MapReduce framework and thus achieves improved classification results. Initially, the database is converted to the probabilistic index table, in which data and attributes are presented in rows and columns, respectively. Then, the membership degree of the unique symbols present in each attribute of data is found. Finally, the proposed FCNB classifier finds the class of data based on training information. The simulation of the proposed FCNB classifier uses the localization and skin segmentation datasets for the purpose of experimentation. The results of the proposed FCNB classifier are analyzed based on the metrics, such as sensitivity, specificity, and accuracy, and compared with the various existing works.