The massive amount of data available in recent years has led to an explosive growth in the field of machine learning. Black box models gain from this, because they can be trained more effectively and provide the best results. In contrast, however, these models are intrinsically less interpretable than other white box models, e.g. a decision tree. With regards to supervised classification problems, where the objective is to assign a class label to a new instance, there are critical applications where interpretability can be a key factor when deciding which model to use or even whether or not to implement a machine learning process. A well-accepted practice to incorporate black box models into these processes is to build a surrogate explainable model that can mimic black box behavior in a neighborhood of the instance whose classification has to be explained. For that purpose, white box models can be used to extract an explanation, defined as both a factual and a counterfactual explanation. A factual explanation is a way to justify the classification of the given instance in a certain category, whereas a counterfactual explanation is a way to understand why that particular instance has not been classified differently. In the literature, we find that these factual and counterfactual explanations are most often built using crisp classifiers. In this work, we propose the use of a fuzzy rule-based system which generates factual and counterfactual explanations by mimicking the behavior of a black box model. This will be done by learning a fuzzy decision tree in a neighborhood of the given instance, which will provide a rule-based system. These rules will be used to extract a factual and a counterfactual explanation. Finally, to maintain the semantics of the problem domain, these rules, learned in a neighborhood of the instance, will be mapped to the global fuzzy sets, defined over the entire range of each variable