  Explainable artificial intelligence is proposed to provide explanations for
reasoning performed by an Artificial Intelligence. There is no consensus on how
to evaluate the quality of these explanations, since even the definition of
explanation itself is not clear in the literature. In particular, for the
widely known Local Linear Explanations, there are qualitative proposals for the
evaluation of explanations, although they suffer from theoretical
inconsistencies. The case of image is even more problematic, where a visual
explanation seems to explain a decision while detecting edges is what it really
does. There are a large number of metrics in the literature specialized in
quantitatively measuring different qualitative aspects so we should be able to
develop metrics capable of measuring in a robust and correct way the desirable
aspects of the explanations. In this paper, we propose a procedure called REVEL
to evaluate different aspects concerning the quality of explanations with a
theoretically coherent development. This procedure has several advances in the
state of the art: it standardizes the concepts of explanation and develops a
series of metrics not only to be able to compare between them but also to
obtain absolute information regarding the explanation itself. The experiments
have been carried out on image four datasets as benchmark where we show REVEL's
descriptive and analytical power.
