Effect of fuzziness in fuzzy rule-based classifiers defined by strong fuzzy partitions and winner-takes-all inference

We study the impact of fuzziness on the behavior of Fuzzy Rule-Based Classifiers (FRBCs) defined by trapezoidal fuzzy sets forming Strong Fuzzy Partitions. In particular, if an FRBC selects the class related to the rule with the highest activation (so-called Winner-Takes-All approach), then fuzziness, as quantified by the slope of the membership functions, has no impact in classifying data in regions of the input space where rules dominate. On the other hand, fuzziness affects the behaviour of the FRBC in regions where the confidence in classification is low. As a consequence, in the context of Explainable Artificial Intelligence, fuzziness is profitable in FRBCs only if classification is accompanied by an explanation of the confidence of the provided outputs.

Automated summary

Fuzziness has an impact on the behavior of Fuzzy Rule-Based Classifiers, but only in regions where the classification confidence is low. Therefore, in Explainable Artificial Intelligence, fuzziness is beneficial in FRBCs only when accompanied by an explanation of the output confidence.