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'Meta-cognitive Radial Basis Function Network' (McRBFN) and its 'Projection Based Learning' (PBL) algorithm for classification problems in sequential framework is proposed in this paper and is referred to as PBL-McRBFN. McRBFN is inspired by human meta-cognitive learning principles. McRBFN has two components, namely the cognitive component and the meta-cognitive component. The cognitive component is a single hidden layer radial basis function network with evolving architecture. In the cognitive component, the PBL algorithm computes the optimal output weights with least computational effort by finding analytical minima of the nonlinear energy function. The meta-cognitive component controls the learning process in the cognitive component by choosing the best learning strategy for the current sample and adapts the learning strategies by implementing self-regulation. In addition, sample overlapping conditions are considered for proper initialization of new hidden neurons, thus minimizes the misclassification. The interaction of cognitive component and meta-cognitive component address the what-to-learn, when-to-learn and how-to-learn human learning principles efficiently. The performance of the PBL-McRBFN is evaluated using a set of benchmark classification problems from UCI machine learning repository and two practical problems, viz., the acoustic emission signal classification and the mammogram for cancer classification. The statistical performance evaluation on these problems has proven the superior performance of PBL-McRBFN classifier over results reported in the literature.