A Study on the Approximation of Clustered Data to Parameterized Family of Fuzzy Membership Functions for the Induction of Fuzzy Decision Trees

This paper investigates the Triangular, Trapezoidal and Gaussian approximation methods for the purpose of induction of Fuzzy Decision Trees (FDT). The generation of FDT is done using a Fuzzy ID3 induction algorithm. In this work three fuzzy partitioning techniques which form the basis for our investigation are given attention, namely Fuzzy C Means clustering (FCM), Grid partitioning and Subtractive clustering (Subclust). Our contribution lies in studying the effect of various approximations on the generation of FDT giving specific attention to the classification accuracy of FDT. In this study we show that the accuracy levels of FDT generated using FCM clustered raw data, bypassing the approximation step, is acceptable and this method has several advantages too. Several computational experiments are conducted and non parametric statistical tests are performed to find if any significant differences exist between the method of bypassing the approximation step and the other methods which include approximation. Ten FDTs are developed and used in this study. These FDT’s differ in their fuzzy partitioning techniques and the approximation methods used.