In order to study the function approximation performance of Fuzzy Neural Networks built up from fuzzy J-K flip-flop neurons a new learning algorithm, the Three Step Bacterial Memetic Algorithm is proposed. Hybrid evolutionary methods that combine genetic type algorithms with "classic" local search have been applied to perform efficient global search. This novel version of the Bacterial Memetic Algorithm with Modified Operator Execution Order (BMAM) is a recently developed technique of hybrid type. This particular merger of evolutionary and gradient based algorithms combining both global and local search consists of bacterial mutation and, as a second step, the Levenberg-Marquardt (LM) method applied for each clone. This LM step saves in this way some potential solutions that could be lost otherwise after each mutation step. As a third step the LM algorithm is recalled for a few iterations for each individual of the population towards reaching the local optimum. In our novel algorithm various kinds of fast algorithm with less complexity, like Quasi-Newton algorithm, Conjugate Gradient algorithm, and two Backpropagation training algorithms: Gradient Descent and Gradient Descent with Adaptive Learning Rate and Momentum are nested in the bacterial mutation.