Optimized Fuzzy Model in Piecewise Interval for Function Approximation
Anup Kumar Mallick, Sumantra Chakraborty, Kabita Purkait, Angsuman Sarkar · International Journal of Electrical and Electronics Engineering · 2024
Function approximation is a technique for estimating an unknown underlying function from input-output instances or examples. Researchers have proposed different methods of function approximations, such as the neural network method, the support vector regression method, the reinforced learning method, the clustering method, the neuro-fuzzy method, etc. This paper introduces a novel data-driven function approximation scheme where the input-output data set is first segmented into multiple pieces. A Mamdani-type fuzzy submodel is constructed for each piece or portion, and the membership functions’ parameters for antecedent and consequent are optimally selected through the differential evolution algorithm. The efficacy of the suggested model is verified on three nonlinear functions, viz., a piecewise polynomial function, an exponentially decreasing sinusoidal function, and an exponentially increasing sinusoidal function. A comparative analysis is done based on the simulation results from the proposed model and the results obtained through the two state-of-the-art function approximation techniques, viz., the support vector regression model and the radial basis function network. The simulation results show that the proposed function approximator has satisfactorily approximated the three functions examined here, surpasses the two state-of-the-art techniques in approximating the two sinusoidal functions, and performs the near-best performance for the piecewise polynomial function. The proposed function approximator is expected to be applied as a new state-of-the-art method for function approximation.