# A Fuzzy Model for Reasoning and Predicting Student's Academic Performance
## 1 Introduction  
Students' academic performance plays an essential role in evaluating and assessing the quality of education. The increasing demands for quality assurance requirements in education have resulted in increasing interest in evaluating and assessing the students' performance. Accordingly, the attention towards the students' academic performance increased from the researchers and application developers. Various fuzzy approaches have been employed to address the uncertainty issues in the students' academic performance. This paper proposes a model (FPM) that reasons and predicts the students' academic performance using fuzzy sets and propositional logic. Fuzzy set is a generalization of the classical set (or the normal mathematical set) which allows the membership function to take values in the interval [0,1] instead of just the membership [1]. Since Fuzzy sets were introduced by [PERSON] in 1965 [1], several theoretical developments have been proposed, such as Pythagorean fuzzy sets [2], intuitionistic fuzzy sets [3], fuzzy logic [4], fuzzy linguistic [5], and fuzzy rough sets [6]. In addition, fuzzy sets concepts were provided considerable additions and contributions in many fields, such as Neuro Fuzzy [7], Fuzzy image processing [8], and Mamdani fuzzy [9]. Propositional logic [10] is a logic representation of knowledge in which the statements are made by propositions. A proposition is a declarative statement which is either true or false, and it allows relationships between the statements to be discovered by logical and mathematical rules. The research on the academic performance field is rapidly increasing. Recently, there are many research works which are concerned with using fuzzy concepts in students' academic performance, whether by providing prediction results, classifying, making decisions, or evaluating and analyzing the students' academic performance, as it is explained in Table 1.  
The following is an overview of these research works. In [11], a neuro-fuzzy model was designed to predict the students' academic performance. The authors designed a fuzzy inference system based on neural networks to assess the students' academic performance. Their experiment was performed with a real dataset obtained from students' achievements in the engineering economy course. They used Quiz (Q), Major (M), Midterm (MD), Final (F), Performance Appraisals (P), and Survey (S) as input parameters for their model and the Students' Academic Performance as output. They expressed these parameters by fuzzy linguistic values such as unsatisfactory (A1), average (A2), good (A3), very well (A4), and excellent (A5). Their neural network structure works on computing these parameters as a gradient vector, which provides a measure of how their model was modeled with the input/output data for a given set of parameters. They showed how several optimization routines can be applied in adjusting the parameters to reduce the error measure (they used sum of the squared error). In [12], a neuro-fuzzy approach was proposed for classifying the students' academic performance. The authors classified students into different groups using a neuro-fuzzy approach. They used a fuzzy classification rule \(R_{i}\): if \(x_{i1}\) is \(A_{i1}\) and \(\cdots\)\(x_{sj}\) is \(A_{ij}\)\(\cdots\) and \(x_{snt}\) is \(A_{int}\), then class is \(C_{k}\), where \(x_{sj}\) represents the \(j\)th feature or input variable of the \(s\)th sample; \(A_{ij}\) denotes the fuzzy set of the \(j\)th feature in the \(i\)th rule; and \(C_{k}\) represents the \(k\)th label of class. They parted the feature space into multiple fuzzy subspaces by fuzzy if-then rules; they represented these fuzzy rules with a network structure. Their neural network classifier contains a multilayer feed-forward network consisting of input, fuzzy membership, fuzzification, defuzzification, normalization, and output.