Fuzzy Conviction Score for Discriminating Decision-Tree-Classified Feature Vectors w.r.t. Relative Distances from Decision Boundaries

We augment decision tree classification analysis with fuzzy membership functions that quantitatively qualify, at each binary decision boundary, the degree of "conviction" to which each data point (i.e. feature vector) is deemed to be on either side of said decision boundary, the further away from the decision threshold, relative to peers, the higher the fuzzy membership value (i.e. the closer to 1). Our fuzzy "conviction" score is analogous to the measure of "confidence" as per traditional statistical methods, whilst handily accommodates the nonlinear discriminant surface created by a decision tree. Although our method has been successfully deployed in confidential commercial setting, here we demonstrate the concept and computation on the benchmark "Breast Cancer Wisconsin (Original/Diagnostic)" Data Sets archived and made available publicly on the UCI (University of California, Irvine) Machine Learning Repository. In addition, we will as well demonstrate that w/o introducing any additional learning loops, our fuzzification of decision tree classifier improves the AUC (Area Under the ROC (Receiver Operating Characteristic) Curve) performance over that of the original decision tree classifier, provided the latter is decently capable of discriminating classes within the relevant data set to begin with.