Multidimensional Fuzzy Transforms with Inverse Distance Weighted Interpolation for Data Regression

The main limitation of the Multidimensional Fuzzy Transform algorithm applied in regression analysis is the fact that it cannot be used if the data are not dense enough with respect to the fuzzy partitions; in these cases, less fine fuzzy partitions must be used to the detriment of the accuracy of the results. In this work, a variation of the Multidimensional Fuzzy Transform regression algorithm is proposed in which the Inverse Distance Weighted interpolation method is applied as a data augmentation algorithm to satisfy the criterion of sufficient data density with respect to the fuzzy partitions. A preprocessing phase determines the optimal values of the parameters to be set in the algorithm's execution. Comparative tests with other well-known regression methods are performed on five regression datasets extracted from the UCI Machine Learning repository. The results show that the proposed method provides the best performance, in terms of regression error reductions.