# An e-Learning Toolbox Based on Rule-Based Fuzzy Approaches
## 4 Results and Discussion
### Didactic Planning Course
#### 4.1.2 Time 2 Model  
Model 2 is identified using the same set of five features available for model 1, plus the initial class plan feature, IC, which can take two possible values, i.e., delivered and not delivered. The results for model 2 are presented in Table 3.  
As a result of the ACEP functionality it can be seen that when a variable directly related to the evaluation process, such as initial class plan (IC), is available, the FIR methodology chooses it as a relevant feature. In this case, the model choses only two features, i.e., IC and AGE, being the first one much more relevant than the second one, i.e., 0.65 vs. 0.35. Notice that this new model has a better prediction performance, with a MSE of 1.04 (see Table 3), lower than the one obtained with the first model of 1.28. Moreover, the classification metrics obtained when the set of rules are used to infer the final mark of the 132 students of the test set are also much better, mainly for the fail and excellent marks. The rules model obtained by the LR-FIR approach defines only one rule for the fail class and another rule for the excellent class. Notice that the specificity is very high, 0.98, meaning that there are very few false positives, i.e., all of the predicted, as non-fail students, at this moment, will not fail at the end of the course, except only two students. On the other hand, the sensitivity is very low, 0.15, meaning that there is a considerable number of students, 17, that at this moment are predicted as non-fail students but they will have a fail mark at the end of the course. Therefore, it is a reminder that they have to keep working throughout the course if they want to get a good mark. The improvement of the prediction performance of model 2 with respect model 1 is significant if we take into account the amount of information available. Notice that the new model added only the first evaluation feature of the course with only two possible values, i.e., delivered or not delivered.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Analysis of the Course Evaluation Process (ACEP)** & & & \\ Relative Relevance of the FIR Model Features: IC = 0.65; AGE = 0.35 & & \\ \hline
**Understanding Students’ Learning Behavior (USLB)** & & & \\ Rules & Sens. & Spec. & Acc. \\ _if_ IC _is_ not delivered _then_ MARK _is_ Fail & 0.15 & 0.98 & 0.86 \\ _if_ IC _is_ delivered _and_ AGE _is_ young _then_ MARK _is_ Excellent & 0.71 & 0.52 & 0.63 \\ _otherwise_ MARK _is_ Pass & 0.41 & 0.67 & 0.59 \\ Macro-average precision: 0.42; Micro-average precision: 0.54 & & \\ \hline
**Assessment of Students’ Learning Performance (ASLP) and Grouping of Students’ Learning Behavior (GSLB)** & & & \\ Mean Square Error: 1.04 & Clustering: Fail 3/20; Pass 16/39; Excellent 52/73 & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: ACEP, USLB, ASLP, and GSLB toolbox results for the model 2 of the didactic planning course. The MARK variable was discretized into three classes: fail (from 0–6), pass (from 6.1–8.9), and excellent (from 9–10). AGE variable was discretized into two classes: young (up to 35) and mature (more than 35). IC variable was discretize, also, into two classes: delivered and not delivered. Spec., Sen., and Acc. stand for specificity, sensitivity, and accuracy, respectively.