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In this paper, two novel kernel based soft computing techniques viz., Differential Evolution trained Kernel Principal Component Wavelet Neural Network (DE-KPCWNN) and DE trained Kernel Binary Quantile Regression (DE-KBQR) are proposed for classification. While, the former can solve multi-class classification problems, the latter can solve binary classification problems only. In the proposed DE-KPCWNN technique, Kernel Principal Component Analysis (KPCA) is applied to input data to get Kernel Principal Components, on which we will employ WNN. Then, DE is used to train the resulting KPCWNN. In DE-KBQR we applied Kernel technique on the input data to get Kernel Matrix, on which we will employ BQR. Then, DE is used to train the resulting KBQR. Several experiments are conducted on four bankruptcy datasets, three benchmark datasets and two Credit scoring datasets to assess the effectiveness of the proposed classification techniques. The results indicate that the proposed Soft Computing hybrids for classification are efficient than the existing classification techniques. Out of the two, DE-KBQR performed relatively better compared to DE-KPCWNN on a majority of binary classification problems. This is the significant outcome of this study.