A fuzzy logic trigger is an alternative approach to triggering a discrete cosine transform or a trigger based on artificial neural networks developed for the surface detector of the Pierre Auger Observatory. The aim of the article is to report on the development of estimators that would allow one distinguishing the signal profiles from the Auger photomultipliers of the water-Cherenkov detectors originating from the neutrino-induced atmospheric showers with a high background of the proton showers. Fuzzy Logic Toolbox provides MATLAB functions, apps, and a Simulink block for analyzing, designing, and simulating systems based on fuzzy logic. The next step is to implement trace recognition algorithms in the FPGA structure to generate a real-time trigger with reasonable use of FPGA resources and with sufficient time margin for 120 MHz sampling. The fuzzy logic trigger will support existing triggers in the Auger surface detector but is optimized to identify neutrino-generated showers. The next step in our research is the simulation of electromagnetic and hadronic cascades in the atmosphere, the propagation of Cherenkov light in the water detector, and the digitalization of the signals in the ADC if the preliminary results obtained from the artificially generated profiles are satisfactory.