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 that it cannot be used if the data are not dense enough concerning the fuzzy partitions; in these cases, less refined fuzzy partitions must be used, to the detriment of the accuracy of the results. In this study, 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 concerning 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 reductions in regression errors.