Fuzzy Logic Function as a Post-hoc Explanator of the Nonlinear
  Classifier
Martin Klimo Lubomir Kralik
Pattern recognition systems implemented using deep neural networks achieve
better results than linear models. However, their drawback is the black box
property. This property means that one with no experience utilising nonlinear
systems may need help understanding the outcome of the decision. Such a
solution is unacceptable to the user responsible for the final decision. He
must not only believe in the decision but also understand it. Therefore,
recognisers must have an architecture that allows interpreters to interpret the
findings. The idea of post-hoc explainable classifiers is to design an
interpretable classifier parallel to the black box classifier, giving the same
decisions as the black box classifier. This paper shows that the explainable
classifier completes matching classification decisions with the black box
classifier on the MNIST and FashionMNIST databases if Zadeh`s fuzzy logic
function forms the classifier and DeconvNet importance gives the truth values.
Since the other tested significance measures achieved lower performance than
DeconvNet, it is the optimal transformation of the feature values to their
truth values as inputs to the fuzzy logic function for the databases and
recogniser architecture used.