Preliminary numerical investigations of conformal predictors based on fuzzy logic classifiers

A new family of techniques, called conformal predictors, have very recently been developed to hedge the estimates of machine learning methods, by providing two parameters, credibility and confidence, which can assess the level of trust that can be attributed to their outputs. In this paper, the main steps required to extend this approach to fuzzy logic classifiers are reported. The more delicate aspect is the definition of an appropriate nonconformity score, which has to be based on the fuzzy membership function to preserve the specificities of Fuzzy Logic. Various examples of increasing complexity are introduced, to describe the main properties of fuzzy logic based conformal predictors and to compare their performance with alternative approaches. The obtained results are quite promising, since conformal predictors based on fuzzy classifiers outperform solutions based on the nearest neighbour in terms of ambiguity, robustness and interpretability.