Defuzzication using polynomial approximation

A new fuzzy inference based on piecewise polynomial interpolation similar to spline technique is proposed. The signed membership function which can encode more information than the usual membership function is also introduced and used together with this new inference method. The fuzzy system using this inference method is more compact compared to other types of fuzzy systems. Online recursive training algorithm is also proposed to tune these polynomials if numerical training data is available. In contrast to neural network where the trained network is only a function of training data, both the heuristic prior knowledge and available training data are used. A simulation example is given to show how this new fuzzy inference can be applied in model reference closed-loop control system