## 1 Introduction  
Deep learning has been very successful in the last decade. Particularly, in domains such as computer vision, deep neural network models have improved their performance significantly over that of Multi-Layer Perceptrons (MLPs), Support Vector Machines (SVMs), Decision Trees (DTs), and ensembles. However, for structured data, deep models do not offer a significant advantage over well-established \"classical\" models, which therefore remain indispensable. A major problem with MLPs is that it is difficult to interpret their responses; MLPs are therefore very often considered as black boxes. However, a number of works aimed at transforming the knowledge stored in connections and activations into propositional rules. [PERSON] et al. introduced a nomenclature encompassing all methods for explaining neural network responses with symbolic rules [1]. For SVMs that are functionally equivalent to MLPs, rule extraction methods were also proposed [2].  
Ensembles of models often provide better accuracy than a single model. Many learning methods for ensembles were introduced, such as bagging [3] and boosting [4]. They have been applied to decision trees and neural networks. However, even decision trees that are models that are directly translatable into propositional rules lose their interpretability when combined in an ensemble. Solving the interpretability problem is crucial for machine learning models to be well accepted by society. For instance, in Europe, with the General Data Protection Regulation (GDPR), an individual has the right to an explanation when an algorithm makes a decision about her or him, such as denying credit. The purpose of this work is to demonstrate that an existing rule extraction technique that is applied to ensembles of neural networks can also be applied to ensembles of decision trees. In addition, our second purpose is to describe the characteristics of the rulesets generated in terms of fidelity, accuracy, and complexity.  
With ensembles of DTs, two main strategies are applied to generate propositional rules. The first tries to reduce the number of DTs by increasing their diversity. Thus, with a reduced number of trees, all of the rules generated by each tree are taken into account. Examples of algorithms for the optimization of diversity are reported in [5]. In the second group of methods, the basic strategy is to remove as many rules as possible. Regarding neural network ensembles, few works have been performed for rule extraction, including the one applied to the DIMLP model (Discretized Interpretable Multi-Layer Perceptron) [6]. Unlike MLPs, in DIMLPs, the discriminative hyperplanes are precisely localized. This makes it possible to define the antecedents of propositional rules. As shown in this work, a DT is transformed into a DIMLP network; hence, the rule extraction technique used for DIMLP ensembles can also be applied to DT ensembles. Specifically, here, this method is applied to Random Forests (RFs) [7] and DT ensembles trained by gradient boosting [8].  
We apply rule extraction to both DT and DIMLP ensembles on eight classification problems. The characteristics of the generated rules are compared to those of \"Skope-Rules\" [9] and other rule extraction techniques. The results obtained by our method were found to be competitive. In the following sections, we briefly present the state of the art of rule extraction from ensembles, the models used, and the experiments, followed by a discussion and the conclusion.