# An e-Learning Toolbox Based on Rule-Based Fuzzy Approaches
## 4 Results and Discussion
### Introductory Course
#### 4.2.4 Time 4 Model  
The last model has available all the features described in Table 6. The toolbox results obtained for this model are summarized in Table 10. As can be seen from the ACEP results, the co-evaluation (COEV) and the final report of the didactic problem (FRDP) are the main assessment events to predict the course performance for each student, with relative relevance values of 0.55 and 0.45, respectively.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Analysis of the Course Evaluation Process (ACEP)** & & & \\ Relative Relevance of the FIR Model Features: COEV = 0.36; H2 = 0.64 & & \\
**Understanding Students’ Learning Behavior (USLB)** & & Sens. & Spec. & Acc. \\ Rules & & 1 & 1 & 1 \\ _if_ H2 _is_ low _then_ MARK _is_ Fail & & 0.81 & 0.86 & 0.83 \\ _if_ COEV _is_ high _and_ H2 _is_ medium _or_ high _then_ MARK _is_ Excellent & & 0.60 & 0.88 & 0.83 \\ _otherwise_ MARK _is_ Pass & & 0.60 & 0.88 & 0.83 \\ \multicolumn{4}{l}{Macro-average precision: 0.80; Micro-average precision: 0.83} \\ \hline
**Assessment of Students’ Learning Performance (ASLP) and Grouping of Students’ Learning** & & & \\
**Behavior (GSLB)** & & & \\ Mean Square Error: 0.094 & Clustering: Fail 9/9; Pass 3/5; Excellent 13/16 & & \\ \hline \hline \end{tabular}
\end{table}
Table 9: ACEP, USLB, ASLP, and GSLB toolbox results for the model 3 of the introductory course. The MARK variable was discretized into three classes: fail (from 0–60), pass (from 61–80), and excellent (from 81–100). H2 and COEV were also discretized into three classes: low (from 0–6), medium (from 6.1–8.9), and high (from 9–10). Spec., Sen., and Acc. stand for specificity, sensitivity, and accuracy, respectively.  
Notice that the rule that represents the set of failing students is based only on the FRDP feature, obtaining a sensitivity, specificity, and accuracy values of 1. Therefore, this rule predicts correctly all the students that fail de course, as already did the first rule of models 2 and 3, using the H2 feature. Therefore, both variables (H2 and FRDP) describe completely this class, providing redundant information. The two rules that describe excellent students obtain better sensitivity and accuracy metrics than the previous models, when applied to the students of the test set. Moreover, the micro-average precision has also slightly increased. The set of rules obtained by the USLB option is simple, comprehensive, and provides new knowledge of the course to teachers and course coordinator. It has also been found in this study, that forum features do not appear in any of the models. Forum activities imply, usually, a significant workload. Teachers and course coordinators can use these results to revise the equation that computes the final mark to obtain a better representation of the knowledge acquired by the students. As shown in Table 10, the reduced MSE of 0.025 demonstrates that the proposed toolbox is capable of accurately capturing students' performance. As previously mentioned, all the failing students are predicted correctly using model 4. For the categories pass and excellent, 2 and 15 students have been correctly predicted, out of 5 and 16, respectively.