## 3 The Proposed System's Architecture
### Student Model
#### 3.2.1 First Layer: Fuzzy Logic System  
In the FB-ITS, the fuzzy logic system is used to determine the student's performance in a particular topic taking two factors into account; the pre-test grade and the topic test grade. These tests are multiple-choice questions used as variables for gathering evidence to update the Bayesian network, which is why these two variables \"Pretest-Grade\" and \"TopicTest-Grade\" used as input variables in the study. On the other hand, the variable student performance in a particular topic of the course material was used as the output of this study, and was utilized as the \"Performance\".  
The \"Pretest-Grade\" is the score of the pre-test given to the student to measure her/his prior knowledge in a particular domain, the \"TopicTest-Grade\" is the score of the test given to the student after completing the study of each topic of course material and the \"Performance\" is the degree of success in a domain topic. A correlating model of the input and output variables is achieved by the established fuzzy rules created by eight faculty members who are experts in the field of computer engineering, and who have taught Excel before. For the input variables, three fuzzy sets are defined for each input variable to describe the student test grade, as it was calculated out of 100 points for both the pre-test and topic test as thus:  
* Poor: the degree of success in the domain topic ranges from 0% to 50%.  
Figure 2: Student model of FB-ITS.  
Good: the degree of success in the domain topic ranges from 40% to 80%.  
Excellent: the degree of success in the domain topic ranges from 70% to 100%.  
Moreover, two fuzzy sets are defined for the output variable to describe the student's performance of a particular topic of the learning material as follows:  
Low: the level of performance in the domain topic ranging from 0% to 80%.  
High: the level of performance in the domain topic ranging from 70% to 100%.  
Each input variable determines three intervals of membership functions. The membership functions of the test grade consist of poor, good, and excellent levels as shown in Figure 3a. An input and output variable is placed in a scale ranging from 0 to 100. Figure 3b shows the membership functions of the output. This membership function includes the low and high of a student's performance in a particular topic.  
In this study, the fuzzy rules are provided by experts. All the rules are configured with two input variables (pretest-Grade and TopicTest-Grade) and one output variable (Performance). Given below are the sets of rules using IF-THEN logic:  
If the (pretest-Grade is poor) and the (TopicTest-Grade is good) then the Performance is Low.  
If the (pretest-Grade is poor) and the (TopicTest-Grade is excellent) then the Performance is High.  
If the (pretest-Grade is good) and the (TopicTest-Grade is poor) then the Performance is Low.  
If the (pretest-Grade is good) and the (TopicTest-Grade is excellent) then the Performance is High.  
If the (pretest-Grade is excellent) and the (TopicTest-Grade is poor) then the Performance is Low.  
If the (pretest-Grade is excellent) and the (TopicTest-Grade is excellent) then the Performance is High.  
Fuzzy rules are triggered after any change in the value of the test result of a particular topic and it updates the performance level of this topic. The output of the fuzzy model is passed to the Bayesian network model as an evidence to update the knowledge level of the related topics.