Effect of number of labels on the accuracy of function approximation

The approximation problem of any nonlinear map using a fuzzy basis function is discussed. This fuzzy basis function (FBF) has the capability of combining both numerical data and linguistic information. The main design objective is to construct an output error for which the number of labels can be varied. In this work, an optimal fuzzy approach is proposed which is capable of matching all the training input-output pairs. The advantage of this approach is that, it produces a simple well-performed method to minimize an objective function in the output error. Simulation results demonstrate the effectiveness of determining the proper number of labels that help drastically in reducing errors between the real function and its representation.