# A Comparative Study of Two Rule-Based Explanation Methods for Diabetic Retinopathy Risk Assessment
## 1 Introduction
Such methods aim to study the relationship between the input and output produced by the system to explain and extract post-hoc explanations. Most of the explanation methods that follow this approach generate a set of inputs, analyse the answers provided by the system to be explained and then create a simpler model from which we can infer an explanation [9; 10; 11]. The most well-known examples of post-hoc ML explanations are Local Interpretable Model-agnostic Explanations (LIME) and Local Rule-Based Explanations (LORE). LIME provides local explanations for a classifier's prediction by fitting a linear regression model locally around the data point of which the prediction is to be explained. LORE generates a set of neighbours of the input point, applies the classification system to them, and builds a decision tree on these results. The explanation obtained by the LORE method is composed of two parts: the activated path, i.e., the rule used to produce the decision, and a set of counterfactual rules which represent the minimal number of changes in the feature values of the instance that would change the conclusion of the system. So, the main difference between LIME and LORE is the neighbourhood generation procedure and the type of explanations each derives. In a previous work [12] we proposed Guided-LORE, an adaptation of the LORE method in which the neighbourhood generation, which is the key in obtaining a solid explanation, was formalised as a search problem and solved using Uniform Cost Search. Such adaptation allowed us, to some extent, to make the generation process more informed. However, we found that both LORE and Guided-LORE did not take into consideration explicitly the case in which the attributes that define the objects are fuzzy. For example, when we use Guided-LORE, a neighbour of a point is generated by adding (or subtracting) a fixed amount (which is called step) to the value of an attribute. We addressed these shortcomings by proposing C-LORE-F (Contextualized LORE for Fuzzy attributes) [13]. If we know that an attribute is fuzzy and we have the information on its fuzzy labels and their associated fuzzy sets, we can make a more focused neighbourhood generation. Based on the definition of the fuzzy sets of each attribute, we can generalise its step from being a fixed value to being a function that depends on that knowledge. In that way, the proposed method is more general. It works in cases where the fuzzy sets associated with the linguistic labels are uniformly or non-uniformly distributed. To the best of our knowledge, that work was the first one that considered such knowledge to develop explanation methods for ML systems based on fuzzy logic, e.g., Fuzzy Decision Trees and Fuzzy Random Forests [14]. In this work, we study two different ways of generating rules in the C-LORE-F method. On one hand, we use the classic crisp decision trees. On the other hand, we propose the construction of preferential decision rules based on rough sets (using the Dominance-Based Rough Set Approach, DRSA, [15]). Both methods are used to generate explanations for the RETIPROGRAM classifier. The rest of this article is structured as follows. Section 2 provides an overview of the related works. In Section 3, we present the two rule explanation methods used in this comparative work. Section 4 presents a general framework for generating counterfactual-based explanations for the RETIPROGRAM classifier. The focus is on the methods for obtaining the decision rules that are used to generate the explanation. In Section 5 we describe the experimentation, including several tests to evaluate and compare the performance of both methods. Finally, in Section 6, we conclude the paper and list some points for future work.