  The use of eXplainable Artificial Intelligence (XAI) systems has introduced a
set of challenges that need resolution. Herein, we focus on how to correctly
select an XAI method, an open questions within the field. The inherent
difficulty of this task is due to the lack of a ground truth. Several authors
have proposed metrics to approximate the fidelity of different XAI methods.
These metrics lack verification and have concerning disagreements. In this
study, we proposed a novel methodology to verify fidelity metrics, using a
well-known transparent model, namely a decision tree. This model allowed us to
obtain explanations with perfect fidelity. Our proposal constitutes the first
objective benchmark for these metrics, facilitating a comparison of existing
proposals, and surpassing existing methods. We applied our benchmark to assess
the existing fidelity metrics in two different experiments, each using public
datasets comprising 52,000 images. The images from these datasets had a size a
128 by 128 pixels and were synthetic data that simplified the training process.
All metric values, indicated a lack of fidelity, with the best one showing a 30
\% deviation from the expected values for perfect explanation. Our
experimentation led us to conclude that the current fidelity metrics are not
reliable enough to be used in real scenarios. From this finding, we deemed it
necessary to development new metrics, to avoid the detected problems, and we
recommend the usage of our proposal as a benchmark within the scientific
community to address these limitations.
