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International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 213-222

Published online June 25, 2022

https://doi.org/10.5391/IJFIS.2022.22.2.213

© The Korean Institute of Intelligent Systems

## Prediction of Students’ Achievements in E-Learning Courses Based on Adaptive Neuro-Fuzzy Inference System

Mithaq Nama Raheema, Ahmed M. Al-Khazzar, and Jabbar Salman Hussain

Department of Prosthetics & Orthotics Engineering, College of Engineering, University of Kerbala, Kerbala, Iraq

Correspondence to :
Ahmed M. Al-Khazzar (ahmed.m.ahmed@uokerbala.edu.iq)

Received: August 21, 2021; Revised: November 15, 2021; Accepted: March 7, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

A prediction of students’ achievements is important for educational organizations. It helps to revise plans and improve students’ achievements throughout their education period. A neurofuzzy system for predicting student achievement is presented in this study. The motivation behind it is to propose a promising achievement predictor for real-time systems associated with e-learning courses. The proposed neuro-fuzzy predictor uses the time that a student needs to answer a question and the difficulty level of that question as input variables. The predictor output was the level of the student’s achievement. Real data were used from e-learning courses at the University of Kerbala, Iraq. The proposed system achieved an excellent accuracy of up to 99% and an root mean square error (RMSE) value of 0.0965 for recognizing unknown test samples. The proposed prediction system based on adaptive neuro-fuzzy inference system(ANFIS) achieved better results than previous techniques. It is hoped that the results of this work will improve college admission processes and support future planning in educational organizations.

Keywords: Machine learning, ANFIS, Adaptive neuro-fuzzy, Student achievement prediction, E-learning

### 1. Introduction

Classification is a method for mapping and categorizing a given dataset into different groups of classes. The objective of a classifier is to predict the desired cluster for each unknown sample in the collected data [1]. Predicting student achievement is an important subject in education [2]. It forecasts the future achievements of students joining a college, thus identifying the students that may obtain poor results and others that may achieve better results. This information can help plan suitable educational services for students and help college administrators in decision-making processes [3]. Estimating the performances of students in the following semester can also aid lecturers in selecting appropriate educational plans for teaching with the goal of improving the students’ results [4]. Another benefit is the development of computerized procedures that can predict academic performance with highly dependable accuracy [5].

Therefore, researchers and lecturers have been interested in predicting educational performance for some time. They tend to identify the most significant factors and their influence through experimental training and analysis, as in [613]. Various typical classification methods have been proposed for student achievement prediction [14,15], such as Bayesian classifiers [16,17], K-means clustering [18], support vector machines (SVM) [16], decision trees [19], and K-nearest neighbors [20]. Other approaches have also been employed in student achievement predictions, such as data mining [21,22], Internet of Things [23], supervised ranking [24], logistic regression [25], multiple regression [26], and supervised learning methods, such as artificial neural networks (ANN) [16,25], and fuzzy inference systems (FIS) [27].

Many hybrid neuro-fuzzy systems have also been employed, such as the adaptive neuro-fuzzy inference system (ANFIS), coactive ANFIS (CANFIS), hierarchical ANFIS (HANFIS), and multiple ANFIS (MANFIS). These hybrid systems have been used in many different applications, such as in [2830], and for student achievement predictions, as in [1,25,3133].

In this study, an ANFIS for predicting the educational achievements of students in e-learning courses is presented. The output of the proposed system is expected to be helpful for college administrators in planning tutoring approaches with the goal of improving the final results. Students who are categorized by ANFIS as having a low level of achievement can receive more motivation and extra teaching to achieve better results in their next semester and final exams.

The main advantage of the model proposed in this work is that a mathematical model is not a pre-condition and that an obtainable input-output dataset of the system is sufficient for building a model. The experimental results obtained from the proposed predictor are very promising for use in real-time systems associated with e-learning courses.

The remainder of this paper is organized into five sections. In Section 2, the theoretical background of the study is presented. The structure of the proposed ANFIS predictor model is explained in Section 3. The results are discussed in Section 4 and the conclusions are presented in Section 5.

ANFIS is a hybrid of ANN and FIS. Therefore, to understand ANFIS, both ANN and FIS have to be understood first. ANN contains several layers of neurons. The connections between neurons are known as synapses. Data are then transferred from the input to the output layer through one or more hidden layers. During the learning process, a set of training data is presented to the network. The network adjusts the synaptic weights of the neurons after processing each training set until the error between the desired and the actual outputs is minimized. The learning process consists of numerous iterations. Each training set contains input values and associative output values [34]. ANNs are typically used to characterize the complicated relationships between the input and output values of datasets [1]. There are three main steps in a classification based on the ANN approach. The first step is data preprocessing, which includes tasks such as normalization, segmentation, and feature selection. The second step is the training of the network to find a map between the input and output datasets and to generate the ANN classifier. The final step is testing with new data to validate the competence of the classifier network [1]. Non-numerical elements in the dataset must be transformed into an appropriate format for training ANN [1].

However, FIS can model the qualitative features of reasoning processes using fuzzy membership functions and human knowledge using IF-THEN rules without employing exact quantitative evaluations [35]. FIS consists of three main steps: fuzzification, rule estimation, and defuzzification. Fuzzification converts crisp inputs into competition grades using linguistic values. Rule estimation forms the IF-THEN rules of knowledge created by experts. Defuzzification converts the fuzzy output of an inference into a result with a crisp value [36].

As influential design methods, ANN and FIS have many advantages, such as the adaptation and learning properties of ANN and the gradual boundary of the data in fuzzy logic and its description using IF-THEN rules for the test system. However, there are some disadvantages to both ANN and FIS, such as the slow training and large amount of data required for ANN [25], and the time-consuming process of describing the fittest membership functions based on trial and error for a fuzzy system [35]. Furthermore, there is no typical procedure for converting human experience or knowledge into a fuzzy rule base [36]. The integration of ANN and fuzzy logic has been identified as a neuro-fuzzy system [25].

This work incorporates ANN and fuzzy logic to achieve the adaptation and learning powers of ANN, together with the knowledge depiction and generalization competences of fuzzy logic in a single hybrid system, called the ANFIS predictor.

ANFIS has effectively been used to model and explore application datasets for determining unknown input-output dependencies and provides beneficial results in many fields [37,39]. Its algorithm can approximate the unknown relationship between a set of given inputs and their associative response variables [31].

This neural network-based structure was then trained using a selected numerical dataset, and the generated fuzzy rules were extracted from the trained neural network [36].

ANFIS can be designed to realize the fuzzy reasoning process, where the parameters of fuzzy reasoning are represented in the connection weights of the neural network [36], typically with five layers. In layer 1, the membership grades for the input vectors are generated at every adaptive node. In layer 2, the activation level is calculated at every fixed node using the product of the incoming signals from layer 1. In layer 3, the normalized firing strength is computed at every fixed node, which is the ratio of the activation level of an individual rule to the entire activation level. In layer 4, the influence of an individual rule on the total output is calculated at every adaptive node using the consequent parameters. In layer 5, the complete output is calculated at a single fixed node, which is the summation of the influences of each rule [25]. Figure 1 shows the ANFIS process of each layer.

### 3.1 Data

In this study, the experimental data consisted of a real dataset of students’ performances from the University of Kerbala. The dataset includes 1, 160 student records, with the structure listed in Table 1. Three variables were selected for the prediction. The first two variables represent independent inputs, and the third element is a dependent output.

The difficulty of each individual question can be classified into one of six levels: very simple, simple, moderate, hard, very hard, and intelligence questions. The average number of students in each department is 145.

The main goal of classification methods is to determine all classes into which the input data are to be categorized, and to allocate each class label. According to the available data from the university and the aim of this study, eight classes were identified, from one to eight, as shown in Table 2.

The collected data may contain inconsistent, missing, and noisy data; therefore, they were prepared to improve their quality. The preparation procedures included identifying outliers and checking the data distribution, processing missing or empty values, and converting the collected data into an analyzable format.

### 3.2 Proposed ANFIS Predictor

The proposed ANFIS is structured as a two-input, one-output model, as shown in Figure 2. The process of each layer is as follows:

For layer 1:

$Out_L1T,i=μTi(T), for i=1, 2, …, 7,Out_L1P,j=μPj(D), for j=1, 2, …, 7,$

where Out_L1T,i and Out_L1D,j are the outputs of layer one for the first input variable (T) and the second input variable (D), respectively. μTi and μDj are membership functions with linguistic values of the linguistic variables (Ti) and (Dj), respectively, such as low, medium, and high. The generalized Bell function is used to calculate the membership values of all linguistic variables, as follows:

$μTi(T)=1/(1+|T-ciai|2bi), for i=1, 2, …, 7,μDj(D)=1/(1+|P-cjaj|2bj), for j=1, 2, …, 7,$

where ci, ai, and bi denote the center, width, and slope of the generalized Bell function, respectively.

For layer 2:

$Out_L2i,j=Wi,j=μTi(T)×μDj(D),for i=1, 2, …, 7, and j=1, 2, …, 7.$

For layer 3:

$Out_L3i,j=W¯i,j=Wi,j/∑1i×jWi,j,for i=1, 2, …, 7, and j=1, 2, …, 7.$

For layer 4:

$Out_L4i,j=fi,jW¯k=fi,j(xi,jTi+yi,jDj+zi,j),for i=1, 2, …, 7, and j=1, 2, …, 7,$

where xi,j, yi,j and zi,j are the consequent parameter set.

For layer 5:

$Out_L5=A=∑1i×jfi,jW¯i,j,for i=1, 2, …, 7, and j=1, 2, …, 7,$

where Out_L5 is the predicted level of a student’s achievement (A).

An appropriate training algorithm for the parameter set should be chosen to achieve the required output prediction. Gradient descent is used to train the network with a cost function of the root mean square error (RMSE), defined as follows:

$RMSE=1N∑i=1N(Ai*-Ai)22,$

where N is the total number of training datasets, $Ai*$ is the desired output, and Ai is the actual output.

The proposed ANFIS predictor was executed by MATLAB 2018b using the fuzzy logic toolbox. This fuzzy system, based on neural learning, requires the following steps:

• The collected data were divided into 70% for training, 15% for validation, and 15% for model testing.

• Two-inputs, and one-output FIS model were generated.

• The designed FIS was trained by the gradient descent method.

• The trained model was validated and tested to predict the next achievements of the students.

The proposed ANFIS was generated and trained using a training dataset. The training iterations continued until the RMSE was reduced to a predetermined value (set to 10−10). Figure 3 shows the error surface of the training process. Each input variable was allocated seven memberships. A set of fuzzy IF-THEN rules was used in fuzzy reasoning to develop conclusions and define the relations between the linguistic parameters of the input and output. For example, “IF T is Low and P is High, THEN A is Middle” is a complete rule that illustrates the reasoning mechanism. Figure 4 shows the reasoning process for the generated Sugeno fuzzy model. The total output is the weighted average of the crisp outputs from the total rules.

Numerous trials have been conducted to evaluate the performance of the proposed ANFIS in predicting students’ achievements. In this work, 49 fuzzy rules were trained with a backpropagation algorithm using 838 training samples to create a set of 7×7 fuzzy models. Subsequently, the trained model was validated and tested with 161 and 161 datasets, respectively, to determine how well the ANFIS model predicts the matching dataset of the output labels. The best modified ANFIS predictor was selected based on the lowest RMSE. The diagnosis rate (DR) was calculated as follows:

$DR=(M/N)×100,$

where M is the total number of correctly predicted test samples with the desired class and N is the total number of test samples. The actual output of the ANFIS predictor represents the expected level of student achievement in the next examination. Figure 5 shows the actual predicted and desired outputs during the training process, and the error between them is shown in Figure 6. The actual output is then rounded to the nearest integer value to show its closeness to the desired output level. The results are of the outputs and the errors between them are shown in Figures 7 and 8, respectively.

The RMSEs for the actual and rounded output values are 0.1467 and 0.0345, respectively. Figure 9 shows the results of the testing process with 322 unknown samples. The prediction was achieved with an excellent diagnosis rate calculated using Eq. (8) as: DR= 319/322 = 99.1%, and with an RMSE value of 0.0965. The RMS results were compared with those of previous works, as shown in Table 3. The smallest RMSE was obtained in this study. Figure 10 shows the confusion matrix for the test process. The trained ANFIS correctly predicted all test samples for levels 1 to 6 and was capable of predicting 60 out of 61 samples for level 7 and 74 out of 76 samples for level 8. This provided prediction accuracies of 100%, 98.4%, and 97.4% for levels 1 to 6, 7, and 8, respectively. This confirms the 99.1% average accuracy of the proposed ANFIS predictor, which is an excellent result when compared with the results of different methods used in other studies, as shown in Table 4. Another evaluation of the effectiveness of the proposed predictor was conducted by comparing the results with those of other studies that used the neuro-fuzzy method, as shown in Table 5. The proposed predictor outperformed other techniques in terms of the performance metrics, such as DR and RMSE.

The potential of using ANFIS in predicting the achievements of students is presented in this work with the aim of enhancing organizational academic planning. Therefore, students who are predicted to obtain level 4 out of 8 and below can receive proper motivation in advance, while students who are predicted to obtain level 5 and above can be supervised with distinct programs designed to maintain and improve their academic achievements.

The presented ANFIS was realized with an accuracy of 99% and an RMSE of 0.0965. Based on these results and a comparison with previous works, as shown in Tables 35, the authors believe that these results are excellent and sufficient to be used as a predictor for students’ achievement levels. This will enable educational organizations to provide improved educational services and support those involved.

The diagnosis rate and prediction accuracy of the system were evaluated by comparing them with those of other studies [1,25,31,4044]. The results verified that the proposed ANFIS predictor is an improvement over other methods. In addition, without a priori information, the settings of the initial parameters of the proposed ANFIS predictor are instinctively rational and perform fast training to capture the dynamics of the underlying system.

The proposed ANFIS predictor uses the subtractive clustering method in the FIS structure, which has a respectable predictive ability. This clustering technique considers every data point as a possible cluster center and determines the degree of the likelihood that it is a cluster center based on the concentration of adjacent data points.

The proposed ANFIS predictor uses a mixed learning process to distinguish the parameters of the Sugeno-FIS. It applies a mixture of the backpropagation gradient descent and least-squares methods to train the parameters of the FIS membership function in mimicking the input-output training dataset.

In this study, the input attributes were the time spent solving the questions and the difficulty levels of the questions, while the output was the student’s achievement. For future work, other factors can be added, such as grades of previous exams, family background factors, and the number of attempts.

The proposed ANFIS predictor has a respectable performance in student achievement prediction as a multi-input single-output (MISO) system. However, in several practical applications of student achievement prediction, there is more than one output, such as “possibility to get scholarship” and “cumulative point average for the following semester.” Thus, as an extension of this work, a multi-input multi-output (MIMO) ANFIS system can be developed for the prediction of other output parameters.

### Conflict of Interest

Fig. 1.

ANFIS process of each layer.

Fig. 2.

Proposed ANFIS structure.

Fig. 3.

Error surface result.

Fig. 4.

ANFIS reasoning process.

Fig. 5.

Actual training output.

Fig. 6.

Error between training outputs.

Fig. 7.

Rounded training outputs.

Fig. 8.

Training error for rounded output.

Fig. 9.

Rounded test outputs.

Fig. 10.

Confusion matrix result.

Table. 1.

Table 1. Structure of dataset elements.

VariableDescriptionDomain
TTime the student spent answering an individual question0–60 seconds
DAverage difficulty of the question50–100 degrees
AAchievement of the student1–8 level

Table. 2.

Table 2. Structure of class output.

OutputClass regionClass description
10–30Fail
231–40Very weak
341–50Weak
451–60Acceptable
561–70Average
671–80Good
781–90Very good
891–100Excellent

Table. 3.

Table 3. RMSE result comparison.

StudyRMSE
Rusli et al. [25]0.3100
Abidin and Dom [31]Training0.0967
Testing01384
This workTraining0.0345
Testing0.0965

Table. 4.

Table 4. Accuracy result comparison with different methods.

StudyClassifierAccuracy (%)
Fahd et al. [40]Random Forest with booster ensemble tuning85.7
Hussain and Khan [41]Genetic algorithm with decision-tree96.64
Alturki and Alturki [42]Random forest92.60
Yousafzai et al. [43]Attention-based BiLSTM90.16
Riyadi Yanto et al. [44]Fuzzy soft set89.00
This workANFIS99.10

Table. 5.

Table 5. Accuracy results comparison with neuro-fuzzy works.

StudyAccuracy (%)
Do and Chen [1]90.03
This work99.10

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Mithq Nama Raheema received a Ph.D. degree in Electrical Engineering from the University of Technology, Iraq. His research interests are AI and smart prostheses.

Ahmed M. Al-Khazzar received a Ph.D. degree in Computer Security from the University of Portsmouth, UK. His research interests are biometrics, AI and smart prostheses.

Jabbar Salman Hussain received a Ph.D. degree in Electrical Engineering from the University of Technology, Iraq. His research interests are AI and smart prostheses.

### Article

#### Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 213-222

Published online June 25, 2022 https://doi.org/10.5391/IJFIS.2022.22.2.213

## Prediction of Students’ Achievements in E-Learning Courses Based on Adaptive Neuro-Fuzzy Inference System

Mithaq Nama Raheema, Ahmed M. Al-Khazzar, and Jabbar Salman Hussain

Department of Prosthetics & Orthotics Engineering, College of Engineering, University of Kerbala, Kerbala, Iraq

Correspondence to:Ahmed M. Al-Khazzar (ahmed.m.ahmed@uokerbala.edu.iq)

Received: August 21, 2021; Revised: November 15, 2021; Accepted: March 7, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

A prediction of students’ achievements is important for educational organizations. It helps to revise plans and improve students’ achievements throughout their education period. A neurofuzzy system for predicting student achievement is presented in this study. The motivation behind it is to propose a promising achievement predictor for real-time systems associated with e-learning courses. The proposed neuro-fuzzy predictor uses the time that a student needs to answer a question and the difficulty level of that question as input variables. The predictor output was the level of the student’s achievement. Real data were used from e-learning courses at the University of Kerbala, Iraq. The proposed system achieved an excellent accuracy of up to 99% and an root mean square error (RMSE) value of 0.0965 for recognizing unknown test samples. The proposed prediction system based on adaptive neuro-fuzzy inference system(ANFIS) achieved better results than previous techniques. It is hoped that the results of this work will improve college admission processes and support future planning in educational organizations.

Keywords: Machine learning, ANFIS, Adaptive neuro-fuzzy, Student achievement prediction, E-learning

### 1. Introduction

Classification is a method for mapping and categorizing a given dataset into different groups of classes. The objective of a classifier is to predict the desired cluster for each unknown sample in the collected data [1]. Predicting student achievement is an important subject in education [2]. It forecasts the future achievements of students joining a college, thus identifying the students that may obtain poor results and others that may achieve better results. This information can help plan suitable educational services for students and help college administrators in decision-making processes [3]. Estimating the performances of students in the following semester can also aid lecturers in selecting appropriate educational plans for teaching with the goal of improving the students’ results [4]. Another benefit is the development of computerized procedures that can predict academic performance with highly dependable accuracy [5].

Therefore, researchers and lecturers have been interested in predicting educational performance for some time. They tend to identify the most significant factors and their influence through experimental training and analysis, as in [613]. Various typical classification methods have been proposed for student achievement prediction [14,15], such as Bayesian classifiers [16,17], K-means clustering [18], support vector machines (SVM) [16], decision trees [19], and K-nearest neighbors [20]. Other approaches have also been employed in student achievement predictions, such as data mining [21,22], Internet of Things [23], supervised ranking [24], logistic regression [25], multiple regression [26], and supervised learning methods, such as artificial neural networks (ANN) [16,25], and fuzzy inference systems (FIS) [27].

Many hybrid neuro-fuzzy systems have also been employed, such as the adaptive neuro-fuzzy inference system (ANFIS), coactive ANFIS (CANFIS), hierarchical ANFIS (HANFIS), and multiple ANFIS (MANFIS). These hybrid systems have been used in many different applications, such as in [2830], and for student achievement predictions, as in [1,25,3133].

In this study, an ANFIS for predicting the educational achievements of students in e-learning courses is presented. The output of the proposed system is expected to be helpful for college administrators in planning tutoring approaches with the goal of improving the final results. Students who are categorized by ANFIS as having a low level of achievement can receive more motivation and extra teaching to achieve better results in their next semester and final exams.

The main advantage of the model proposed in this work is that a mathematical model is not a pre-condition and that an obtainable input-output dataset of the system is sufficient for building a model. The experimental results obtained from the proposed predictor are very promising for use in real-time systems associated with e-learning courses.

The remainder of this paper is organized into five sections. In Section 2, the theoretical background of the study is presented. The structure of the proposed ANFIS predictor model is explained in Section 3. The results are discussed in Section 4 and the conclusions are presented in Section 5.

### 2. Theory

ANFIS is a hybrid of ANN and FIS. Therefore, to understand ANFIS, both ANN and FIS have to be understood first. ANN contains several layers of neurons. The connections between neurons are known as synapses. Data are then transferred from the input to the output layer through one or more hidden layers. During the learning process, a set of training data is presented to the network. The network adjusts the synaptic weights of the neurons after processing each training set until the error between the desired and the actual outputs is minimized. The learning process consists of numerous iterations. Each training set contains input values and associative output values [34]. ANNs are typically used to characterize the complicated relationships between the input and output values of datasets [1]. There are three main steps in a classification based on the ANN approach. The first step is data preprocessing, which includes tasks such as normalization, segmentation, and feature selection. The second step is the training of the network to find a map between the input and output datasets and to generate the ANN classifier. The final step is testing with new data to validate the competence of the classifier network [1]. Non-numerical elements in the dataset must be transformed into an appropriate format for training ANN [1].

However, FIS can model the qualitative features of reasoning processes using fuzzy membership functions and human knowledge using IF-THEN rules without employing exact quantitative evaluations [35]. FIS consists of three main steps: fuzzification, rule estimation, and defuzzification. Fuzzification converts crisp inputs into competition grades using linguistic values. Rule estimation forms the IF-THEN rules of knowledge created by experts. Defuzzification converts the fuzzy output of an inference into a result with a crisp value [36].

As influential design methods, ANN and FIS have many advantages, such as the adaptation and learning properties of ANN and the gradual boundary of the data in fuzzy logic and its description using IF-THEN rules for the test system. However, there are some disadvantages to both ANN and FIS, such as the slow training and large amount of data required for ANN [25], and the time-consuming process of describing the fittest membership functions based on trial and error for a fuzzy system [35]. Furthermore, there is no typical procedure for converting human experience or knowledge into a fuzzy rule base [36]. The integration of ANN and fuzzy logic has been identified as a neuro-fuzzy system [25].

This work incorporates ANN and fuzzy logic to achieve the adaptation and learning powers of ANN, together with the knowledge depiction and generalization competences of fuzzy logic in a single hybrid system, called the ANFIS predictor.

ANFIS has effectively been used to model and explore application datasets for determining unknown input-output dependencies and provides beneficial results in many fields [37,39]. Its algorithm can approximate the unknown relationship between a set of given inputs and their associative response variables [31].

This neural network-based structure was then trained using a selected numerical dataset, and the generated fuzzy rules were extracted from the trained neural network [36].

ANFIS can be designed to realize the fuzzy reasoning process, where the parameters of fuzzy reasoning are represented in the connection weights of the neural network [36], typically with five layers. In layer 1, the membership grades for the input vectors are generated at every adaptive node. In layer 2, the activation level is calculated at every fixed node using the product of the incoming signals from layer 1. In layer 3, the normalized firing strength is computed at every fixed node, which is the ratio of the activation level of an individual rule to the entire activation level. In layer 4, the influence of an individual rule on the total output is calculated at every adaptive node using the consequent parameters. In layer 5, the complete output is calculated at a single fixed node, which is the summation of the influences of each rule [25]. Figure 1 shows the ANFIS process of each layer.

### 3.1 Data

In this study, the experimental data consisted of a real dataset of students’ performances from the University of Kerbala. The dataset includes 1, 160 student records, with the structure listed in Table 1. Three variables were selected for the prediction. The first two variables represent independent inputs, and the third element is a dependent output.

The difficulty of each individual question can be classified into one of six levels: very simple, simple, moderate, hard, very hard, and intelligence questions. The average number of students in each department is 145.

The main goal of classification methods is to determine all classes into which the input data are to be categorized, and to allocate each class label. According to the available data from the university and the aim of this study, eight classes were identified, from one to eight, as shown in Table 2.

The collected data may contain inconsistent, missing, and noisy data; therefore, they were prepared to improve their quality. The preparation procedures included identifying outliers and checking the data distribution, processing missing or empty values, and converting the collected data into an analyzable format.

### 3.2 Proposed ANFIS Predictor

The proposed ANFIS is structured as a two-input, one-output model, as shown in Figure 2. The process of each layer is as follows:

For layer 1:

$Out_L1T,i=μTi(T), for i=1, 2, …, 7,Out_L1P,j=μPj(D), for j=1, 2, …, 7,$

where Out_L1T,i and Out_L1D,j are the outputs of layer one for the first input variable (T) and the second input variable (D), respectively. μTi and μDj are membership functions with linguistic values of the linguistic variables (Ti) and (Dj), respectively, such as low, medium, and high. The generalized Bell function is used to calculate the membership values of all linguistic variables, as follows:

$μTi(T)=1/(1+|T-ciai|2bi), for i=1, 2, …, 7,μDj(D)=1/(1+|P-cjaj|2bj), for j=1, 2, …, 7,$

where ci, ai, and bi denote the center, width, and slope of the generalized Bell function, respectively.

For layer 2:

$Out_L2i,j=Wi,j=μTi(T)×μDj(D),for i=1, 2, …, 7, and j=1, 2, …, 7.$

For layer 3:

$Out_L3i,j=W¯i,j=Wi,j/∑1i×jWi,j,for i=1, 2, …, 7, and j=1, 2, …, 7.$

For layer 4:

$Out_L4i,j=fi,jW¯k=fi,j(xi,jTi+yi,jDj+zi,j),for i=1, 2, …, 7, and j=1, 2, …, 7,$

where xi,j, yi,j and zi,j are the consequent parameter set.

For layer 5:

$Out_L5=A=∑1i×jfi,jW¯i,j,for i=1, 2, …, 7, and j=1, 2, …, 7,$

where Out_L5 is the predicted level of a student’s achievement (A).

An appropriate training algorithm for the parameter set should be chosen to achieve the required output prediction. Gradient descent is used to train the network with a cost function of the root mean square error (RMSE), defined as follows:

$RMSE=1N∑i=1N(Ai*-Ai)22,$

where N is the total number of training datasets, $Ai*$ is the desired output, and Ai is the actual output.

The proposed ANFIS predictor was executed by MATLAB 2018b using the fuzzy logic toolbox. This fuzzy system, based on neural learning, requires the following steps:

• The collected data were divided into 70% for training, 15% for validation, and 15% for model testing.

• Two-inputs, and one-output FIS model were generated.

• The designed FIS was trained by the gradient descent method.

• The trained model was validated and tested to predict the next achievements of the students.

The proposed ANFIS was generated and trained using a training dataset. The training iterations continued until the RMSE was reduced to a predetermined value (set to 10−10). Figure 3 shows the error surface of the training process. Each input variable was allocated seven memberships. A set of fuzzy IF-THEN rules was used in fuzzy reasoning to develop conclusions and define the relations between the linguistic parameters of the input and output. For example, “IF T is Low and P is High, THEN A is Middle” is a complete rule that illustrates the reasoning mechanism. Figure 4 shows the reasoning process for the generated Sugeno fuzzy model. The total output is the weighted average of the crisp outputs from the total rules.

### 4. Results

Numerous trials have been conducted to evaluate the performance of the proposed ANFIS in predicting students’ achievements. In this work, 49 fuzzy rules were trained with a backpropagation algorithm using 838 training samples to create a set of 7×7 fuzzy models. Subsequently, the trained model was validated and tested with 161 and 161 datasets, respectively, to determine how well the ANFIS model predicts the matching dataset of the output labels. The best modified ANFIS predictor was selected based on the lowest RMSE. The diagnosis rate (DR) was calculated as follows:

$DR=(M/N)×100,$

where M is the total number of correctly predicted test samples with the desired class and N is the total number of test samples. The actual output of the ANFIS predictor represents the expected level of student achievement in the next examination. Figure 5 shows the actual predicted and desired outputs during the training process, and the error between them is shown in Figure 6. The actual output is then rounded to the nearest integer value to show its closeness to the desired output level. The results are of the outputs and the errors between them are shown in Figures 7 and 8, respectively.

The RMSEs for the actual and rounded output values are 0.1467 and 0.0345, respectively. Figure 9 shows the results of the testing process with 322 unknown samples. The prediction was achieved with an excellent diagnosis rate calculated using Eq. (8) as: DR= 319/322 = 99.1%, and with an RMSE value of 0.0965. The RMS results were compared with those of previous works, as shown in Table 3. The smallest RMSE was obtained in this study. Figure 10 shows the confusion matrix for the test process. The trained ANFIS correctly predicted all test samples for levels 1 to 6 and was capable of predicting 60 out of 61 samples for level 7 and 74 out of 76 samples for level 8. This provided prediction accuracies of 100%, 98.4%, and 97.4% for levels 1 to 6, 7, and 8, respectively. This confirms the 99.1% average accuracy of the proposed ANFIS predictor, which is an excellent result when compared with the results of different methods used in other studies, as shown in Table 4. Another evaluation of the effectiveness of the proposed predictor was conducted by comparing the results with those of other studies that used the neuro-fuzzy method, as shown in Table 5. The proposed predictor outperformed other techniques in terms of the performance metrics, such as DR and RMSE.

### 5. Conclusion

The potential of using ANFIS in predicting the achievements of students is presented in this work with the aim of enhancing organizational academic planning. Therefore, students who are predicted to obtain level 4 out of 8 and below can receive proper motivation in advance, while students who are predicted to obtain level 5 and above can be supervised with distinct programs designed to maintain and improve their academic achievements.

The presented ANFIS was realized with an accuracy of 99% and an RMSE of 0.0965. Based on these results and a comparison with previous works, as shown in Tables 35, the authors believe that these results are excellent and sufficient to be used as a predictor for students’ achievement levels. This will enable educational organizations to provide improved educational services and support those involved.

The diagnosis rate and prediction accuracy of the system were evaluated by comparing them with those of other studies [1,25,31,4044]. The results verified that the proposed ANFIS predictor is an improvement over other methods. In addition, without a priori information, the settings of the initial parameters of the proposed ANFIS predictor are instinctively rational and perform fast training to capture the dynamics of the underlying system.

The proposed ANFIS predictor uses the subtractive clustering method in the FIS structure, which has a respectable predictive ability. This clustering technique considers every data point as a possible cluster center and determines the degree of the likelihood that it is a cluster center based on the concentration of adjacent data points.

The proposed ANFIS predictor uses a mixed learning process to distinguish the parameters of the Sugeno-FIS. It applies a mixture of the backpropagation gradient descent and least-squares methods to train the parameters of the FIS membership function in mimicking the input-output training dataset.

In this study, the input attributes were the time spent solving the questions and the difficulty levels of the questions, while the output was the student’s achievement. For future work, other factors can be added, such as grades of previous exams, family background factors, and the number of attempts.

The proposed ANFIS predictor has a respectable performance in student achievement prediction as a multi-input single-output (MISO) system. However, in several practical applications of student achievement prediction, there is more than one output, such as “possibility to get scholarship” and “cumulative point average for the following semester.” Thus, as an extension of this work, a multi-input multi-output (MIMO) ANFIS system can be developed for the prediction of other output parameters.

### Fig 1.

Figure 1.

ANFIS process of each layer.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 2.

Figure 2.

Proposed ANFIS structure.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 3.

Figure 3.

Error surface result.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 4.

Figure 4.

ANFIS reasoning process.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 5.

Figure 5.

Actual training output.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 6.

Figure 6.

Error between training outputs.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 7.

Figure 7.

Rounded training outputs.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 8.

Figure 8.

Training error for rounded output.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 9.

Figure 9.

Rounded test outputs.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

### Fig 10.

Figure 10.

Confusion matrix result.

The International Journal of Fuzzy Logic and Intelligent Systems 2022; 22: 213-222https://doi.org/10.5391/IJFIS.2022.22.2.213

Structure of dataset elements.

VariableDescriptionDomain
TTime the student spent answering an individual question0–60 seconds
DAverage difficulty of the question50–100 degrees
AAchievement of the student1–8 level

Structure of class output.

OutputClass regionClass description
10–30Fail
231–40Very weak
341–50Weak
451–60Acceptable
561–70Average
671–80Good
781–90Very good
891–100Excellent

RMSE result comparison.

StudyRMSE
Rusli et al. [25]0.3100
Abidin and Dom [31]Training0.0967
Testing01384
This workTraining0.0345
Testing0.0965

Accuracy result comparison with different methods.

StudyClassifierAccuracy (%)
Fahd et al. [40]Random Forest with booster ensemble tuning85.7
Hussain and Khan [41]Genetic algorithm with decision-tree96.64
Alturki and Alturki [42]Random forest92.60
Yousafzai et al. [43]Attention-based BiLSTM90.16
Riyadi Yanto et al. [44]Fuzzy soft set89.00
This workANFIS99.10

Accuracy results comparison with neuro-fuzzy works.

StudyAccuracy (%)
Do and Chen [1]90.03
This work99.10

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