## 3 The Proposed System's Architecture
### Student Model
#### 3.2.2 Second Layer: Bayesian Network  
This study uses the Microsoft Bayesian network Toolkit (MSBNx) to construct the Bayesian network model, which is a component-based Windows application for creating and evaluating Bayesian networks [42]. Where the Bayesian network in FB-ITS is implemented by MSBNx, the Excel topics network can be easily modified to address another learning domain. In FB-ITS, the Bayesian network model consists of 11 nodes, which represent the topics of the Excel course. A total of 11 topic titles were grouped in terms of the Excel course content, according to the syllabus of Introduction to Computers and Information Systems course (CMPE 105). Figure 3: (**a**) The membership functions of the test grade, (**b**) The membership functions of the output. The dependencies existing among the course topics can be represented as prerequisite relationships. For instance, Topic-1 has to be learned before Topic-2, because understanding Topic-1 is a prerequisite to understanding Topic-2. The node of Topic-1 being depended upon is also called the pre-requisite node. The entire DAG of the Bayesian network implemented in the FB-ITS is shown in Figure 4.  
After constructing the Bayesian network, a conditional probability distribution (CPD) table is designed for each topic node, taking its parents in the network into account. In this work, all CPDs values were obtained by the experts and the experience of instructors. These probability values will then be used by the model for inference about the problem. The CPD value for Y given X is denoted by P(Y|X). In the context of Excel topics, the probability of a student having learned topic-1 (Excel Environment) is denoted by P(Topic-1). Moreover, the probability of a student having learned Topic-2 given Topic-1 is denoted by P(Topic-2|Topic-1). P(Topic-2 = Learned/Topic-1 = Learned) is the probability that the student has learned Topic-2 given evidence that the prerequisite Topic-1 has been learned. The primary purpose of tracking a student's behavior during the interaction with the system is to collect evidence to update the Bayesian network model, where the evidence is the already observed information about this student. Several assessment approaches are used to collect evidence to update the Bayesian network, such as the student's direct responses or his/her answers to the exam questions. Furthermore, some systems include the student's performance scores, time spent on questions, sequences of reading pages or reading times to enhance the student's assessment. In this study, the fuzzy logic system is used to collect the evidence taking into account the prior and current knowledge in a particular topic. The main purpose of the Bayesian network model is to predict the KL of related topics and to identify which topic is ready to be learned and which are not based on the probability. For each topic node in the Bayesian network model, there are two states: learned or not learned by the student. The learned state of certain topics in the Excel course can be assessed by calculating the posterior probability P(topic = learned/evidence), where the evidence is the student's performance on a prerequisite topic obtained from the fuzzy logic model. If the posterior probability of the topic is greater than or is equal to a certain threshold (this work defines it as being equal to 0.8), this topic is marked as \"Learned\". Otherwise, the topic is marked as \"notLearned\". The threshold choosed by the experts as 0.8 because Atilim University uses European Credit Transfer System (ECTS) (https://ec. Figure 4: Bayesian network implemented in FB-ITS. europa.eu/education/resources-and-tools/european-credit-transfer-and-accumulation-system-ects) as an internal credit accumulation system, in accordance with the Bologna Process. According to this system, the percentage 80 means the status is \"Good\" and the grade point is 3.00 over 4.00.