A trainable transparent universal approximator for defuzzification in Mamdani-type neuro-fuzzy controllers

A novel technique of designing application specific defuzzification strategies with neural learning is presented. The proposed neural architecture considered as a universal defuzzification approximator is validated by showing the convergence when approximating several existing defuzzification strategies. The method is successfully tested with fuzzy controlled reverse driving of a model truck. The transparent structure of the universal defuzzification approximator allows us to analyze the generated customized defuzzification method using the existing theories of defuzzification. The integration of universal defuzzification approximator instead of traditional methods in Mamdani-type fuzzy controllers can also be considered as an addition of trainable nonlinear noise to the output of the fuzzy rule inference before calculating the defuzzified crisp output. Therefore, nonlinear noise trained specifically for a given application shows a grade of confidence on the rule base, providing an additional opportunity to measure the quality of the fuzzy rule base. The possibility of modeling a Mamdani-type fuzzy controller as a feedforward neural network with the ability of gradient descent training of the universal defuzzification approximator and antecedent membership functions fulfil the requirement known from multilayer preceptrons in finding solutions to nonlinear separable problems.