**5. Discussions**

Discussions about the results obtained by the model are carried out based on the interpretability criteria to be evaluated in eFNN-SODA. This is required to ensure that the information extraction stated below is trustworthy and coherent, in addition to verifying the accuracy findings.

The results obtained by the model present factors that can be interpreted through fuzzy rules that solve the target problem. The fuzzy rules were validated concerning the criteria of simplicity (fewer rules with greater accuracy), distinguishability (not similar), consistency, with coverage in all samples evaluated, and that meet the criteria of completeness. Through these generated fuzzy rules, it is possible to identify and analyze their antecedents and consequents and the relationship between them, and finally, it is possible to identify the evolution of the model through the creation of new fuzzy rules.

An interpretive evaluation of fuzzy rules leads us to identify that all dimensions of the problem (except successive outbidding) have similar final relevance values for separating fraudulent behavior from normal behavior. This indicates that there is not such a clear separability between the two groups of samples in these dimensions. The evolving behavior of the weights (Figure 13) also demonstrates stability in the order of relevance of the features of the problem. They did not change their position of relevance throughout the experiment. The second highest weight value for the feature weight technique is the Bidding Ratio of 0.59. This demonstrates that, except for the Successive Outbidding dimension, all the others involved in the problem have poorly separable samples according to the Dy–Brodley separability criteria.

The comparison of interpretability extracted by the eFNN-SODA model and the Fuzzy Hoeffding Decision Tree model (Figure 16) has some similarities and distinctions. The tree model is easier for visualizing the relationships, but the fuzzy rule model is closer to human reasoning. Regarding their similarities to the root of the tree shown in Figure 16 that has the Successive Outbidding as its central dimension, other nodes arise for the following evaluations. This corroborates that this is the first value to be analyzed in the tree, thus being the most relevant dimension. The generated fuzzy rules also identify this factor, as Successive Outbidding significantly impacts rule antecedents.

The three most relevant dimensions to the problem were determined based on the fuzzy rules generated. With them, it is possible to elaborate future studies and technological tools that can avoid Successive Outbidding, Bidding Ratio, and Winning Ratio considered fraudulent. Successive Outbidding Technologies to avoid subsequent bids can be implemented in digital solutions that provide auction services. For example, if the fuzzy neural network identifies a user at high risk of fraud, they cannot place successive bids for a certain period. In the same way, when possible fraud in the bids is identified, they may undergo an audit (human or through some expert system) or be the subject of extra validation, such as the confirmation of some data or limitation on the number of bids that they can give for a product until their veracity is proven. Finally, different mechanisms can be provided for Winning Ratio fraud if the fuzzy neural network identifies that that winner has a fraudulent profile.
