In this work, we study blind equalization techniques to mitigate inter-symbol interference (ISI), and blind sources separation (BSS) in multiple inputs multiple outputs (MIMO) communication systems. Mainly, we are interested in the multiuser generic blind equalizer (MU-GBE). A MU-GBE has no prior information about the transmission channels and the used constellations. To solve this challenge, a joint MU-GBE, based on a new multi-criteria cost function and automatic modulation classification (AMC) is proposed. The new multi-users multi-criteria cost function is based on the probability density fitting (PDF) and the Knearest neighbors (KNN) algorithm is considered for the AMC stage. This approach is implemented in its linear and nonlinear versions. For the nonlinear case, we use a neural network. Numerical results, in terms of mean square error (MSE) and symbol error rate (SER) with quadrature amplitude modulation (QAM) signals show that our multi users multi-criteria GBE is effective in alleviating the ISI.