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In this paper, we study blind equalization techniques to mitigate inter-symbol interference (ISI), and mainly, we are focused on generic blind equalizer (GBE). A GBE has no prior information about the transmission channel or the used constellation. To solve this challenge, a joint generic blind equalizer, based on a new multi-criteria cost function and automatic modulation classification (AMC) is proposed. The new multi-criteria cost function is based on the probability density fitting (PDF) and the k-nearest neighbor (KNN) algorithm is used for the AMC stage. Thus, using a neural architecture, the new criterion is demonstrated in its linear and nonlinear context. Simulation results support our claims with Quadrature Amplitude Modulation (QAM) transmitted signals in single input single output (SISO) communication system and they show a better performance in terms of mean square error (MSE) and symbol error rate (SER) compared to other GBE from the literature.