This paper introduces a novel hybrid algorithm for function approximation. The proposed algorithm consists of a hybrid approach to develop Takagi and Sugeno's fuzzy model for function approximation. In this paper, a coarse tuning based on Takagi and Sugeno's fuzzy model is applied to identify the fuzzy structure, and also a fuzzy cluster validity index is utilized to determine the optimal number of clusters. To obtain a more precision model, genetic algorithm (GA) and particle swarm optimization (PSO) are performed to conduct fine-tuning for the obtained parameter set of the premise parts and consequent parts in the aforementioned fuzzy model. The proposed algorithm is successfully applied to three tested examples. Compared with other existing approaches in the literature, the proposed algorithm is very useful for modeling function approximation.
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