# An e-Learning Toolbox Based on Rule-Based Fuzzy Approaches
## 4 Results and Discussion
### Didactic Planning Course
#### 4.1.4 Time 4 Model  
The model at time 4 corresponds to the end of the course. At this point, the complete set of 13 features are available (see Table 1) and are used to obtain the last FIR model. The results for this model are presented in Table 5. As can be seen from the ACEP results, the variables with the most influence on the prediction of a student's final mark are the co-evaluation (COEV), the initial class plan (IC), and the experience report (ER), with relevance values of 0.32, 0.33, and 0.35, respectively. These three variables alone account for 50% of the evaluation of the final grade. It is important to mention, that although variables FC (final class plan) and BR (work performed in the branch) constitute a 35% of the final grade, the FIR optimal model has not selected them as relevant. From these results, it can be concluded that they are highly correlated with COEV, IC, and ER, meaning that they contain redundant information. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Analysis of the Course Evaluation Process (ACEP)** & & & \\ Relative Relevance of the FIR Model Features: COEV = 0.36; IC = 0.34; FC = 0.30 & & \\ \hline
**Understanding students’ learning behavior (USLB)** & & & \\ Rules & & & \\ _if_ COEV is medium or high _and_ FC _is_ high _and_ IC _is_ not delivered _then_ MARK _is_ Pass & & \\ _if_ FC _is_ high _and_ IC _is_ delivered _then_ MARK _is_ Pass & & \\ _if_ COEV is_ medium or high _and_ FC _is_ high _and_ IC _is_ delivered _then_ MARK _is_ Excellent _otherwise_ MARK _is_ Fail & 0.65 & 0.97 & 0.92 \\ Macro-average precision: 0.70; Micro-average precision: 0.73 & & & \\ \hline \hline
**Assessment of Students’ Learning Performance (ASLP) and Grouping of Students’ Learning Behavior (GSLB)** & & & \\ Mean Square Error: 0.32 & Clustering: Fail 12/20; Pass 25/39; Excellent 59/73 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ACEP, USLB, ASLP, and GSLB toolbox results for the model 3 of the didactic planning course. The MARK variable was discretized into three classes: fail (from 0–6), pass (from 6.9–8.9), and excellent (from 9–10). FC and COEV were discretized into three classes: low (from 0–5), medium (from 5.1–7.9), and high (from 8–10). IC variable was discretize, also, into two classes: delivered and not delivered. Spec., Sen., and Acc. stand for specificity, sensitivity, and accuracy, respectively. As highlighted in the introduction, the evaluation process is, probably, the most time-consuming task for the teacher. The results obtained by the ACEP option can be used by the advisors to analyze and, if necessary, adapt the evaluation events that make up the final grade. The redundancy identified by the FIR model in some assessment events allows teachers to better organize the correction load, e.g., delegate the correction of the redundant evaluation acts to an assistant. The set of rules obtained by the USLB option are simple, comprehensive, and are validated by teachers and course coordinator during the modeling phase. The rules are used to infer the final mark for the 132 students of the test set, obtaining high values of sensitivity, specificity, and accuracy. Moreover, macro and micro-average precisions are, also, quite high and have similar values, meaning good precision at, both, class and instance levels. Remember that macro-average gives equal weight to each class, whereas micro-average gives equal weight to each instance. In our case, where the multi-class classification problem is imbalanced, the micro-average precision is a more relevant metric. It can be seen that the model obtains a high level of accuracy since the MSE has been reduced to a value of 0.09. This model is able to predict 16 failing students (out of 20), 28 pass students (out of 39), and 67 excellent students (out of 73). The four students that failed, and were not predicted by the model as failing students, were predicted as pass students, and none of them were predicted as excellent students.