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Three new learning algorithms for Takagi-Sugeno-Kang fuzzy system based on training error and genetic algorithm are proposed. The first two algorithms are consisted of two phases. In the first phase, the initial structure of neuro-fuzzy network is created by estimating the optimum points of training data in input-output space using KNN (for the first algorithm) and Mean-Shift methods (for the second algorithm) and keeps adding new neurons based on an error-based algorithm. Then in the second phase, redundant neurons are recognized and removed using a genetic algorithm. The third algorithm then builds the network in one phase using a modified version of error algorithm used in the first two methods. The KNN method is shown to be invariant to parameter K in KNN algorithm and in two simulated examples outperforms other neuro-fuzzy approaches in both performance and network compactness.