The handling of big data refers efficient management of processing and storage requirements of very large volume of structured and an unstructured data of association. The basic approach for big data classification using naïve Bayes classifier is extended with correlation among the attributes so that it becomes a dependent hypothesis, and it is named as correlative naïve Bayes classifier (CNB). The optimization algorithms such as cuckoo search and grey wolf optimization are integrated with the correlative naïve Bayes classifier, and significant performance improvement is achieved. This model is called as cuckoo grey wolf correlative naïve Bayes classifier (CGCNB). The further performance improvements are achieved by incorporating fuzzy theory termed as fuzzy correlative naïve Bayes classifier (FCNB) and holoentropy theory termed as Holoentropy correlative naïve Bayes classifier (HCNB), respectively. FCNB and HCNB classifiers are comparatively analyzed with CNB and CGCNB and achieved noticeable performance by analyzing with accuracy, sensitivity and specificity analysis. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.