Neutrosophic Optimization and Intelligent systems Journal Homepage: sciencesforce.com/nois Neutrosophic Opt. Int. Syst. Vol. 2 (2024) 7–18 Paper Type: Original Article Assessing Students Performance Using Neutrosophic Tool Sunday Adesina Adebisi 1,* , and Said Broumi 2 Department of Mathematics, Faculty of Science, University of Lagos, Nigeria; adesinasunday@yahoo.com. Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco; broumisaid78@gmail.com; s.broumi@flbenmsik.ma. 1 2 Received: 13 Nov 2023 Revised: 31 Jan 2024 Accepted: 06 Mar 2024 Published: 16 Mar 2024 Abstract Recently, a lot of educational as well as academic researchers have shown their ultimate interest in educational data mining techniques. Thus, several studies that can definitely contribute to the improvement of the educational process are conducted. The results of this lead to several issues that have to be addressed if the students general academic performances are to be improved. In this paper, we investigate the academic performance of a set of students in their core subjects. This we did by using the concept of the neutrosophic frequency, as well as the neutrosophic relative frequency distribution for the class of scores for the set of students. The results give some form of expectation for their general performance. This case serves as a means to enhance the educational process of the chosen set of students by identifying the students at risk of failure or dropping out and predicting the students' academic level at an early stage to provide the necessary support for the at-risk students. Keywords: Neutrosophic Statistics, Classical Statistics, Crisp Numbers, Neutrosophic Frequency, Netrosophic Relative Frequency. 1 |Introduction In recent years, eminent and passionate researchers in the field of educational developments have indicated their ultimate interest in educational data mining techniques. Thus, several studies that can definitely contribute to the improvement of the educational process are conducted. The results of this lead to several issues that have to be addressed if the students general academic performances are to be improved. In this paper, we investigate the academic performance of a set of students in their core subjects. This we did by using the concept of the neutrosophic frequency as well as the neutrosophic relative frequency distribution for the class of scores for the set of students. The results give some form of expectation for their general performance. This exercise serves as a means to enhance the educational process of the chosen set of students by identifying the students at risk of failure or dropping out and predicting the students' academic level at an early stage to provide the necessary support for the at-risk students [10]. Studies involving the exploitation of the concepts and techniques of neutrosophic inference that rely on neutrosophic logic are very useful in evaluating the level of human resource performance in economics, institutions, and other working enterprises, such as in the field of food industries. This logic is an extension of fuzzy logic and is characterized by its Corresponding Author: adesinasunday@yahoo.com 10. https://doi.org/10.61356/j.nois.2024.212989 Licensee Neutrosophic Optimization and Intelligent systems. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0). Assessing Students Performance Using Neutrosophic Tool 8 ability to deal with indeterminate information that carries different degrees of truth, falsehood, neutrality, and uncertainty. This can be further followed by the application of computer software, which produces a neutrosophic inference system for human resource data that can be related to qualifications, experiences, skills, productivity, absence, discipline, and others. In [6] (Haitham I. A. Ward et al., 2023), data were converted into neutrosophic values using membership, comparison, and action functions. Then neutrosophic rules were used to calculate human resource performance scores in terms of truth, falsehood, neutrality, and uncertainty. The results of the study showed that the level of human resource performance in the institution was average in general. Hence, based on their results, some recommendations were presented in order to improve human resource performance in the institution, such as developing training, motivation, evaluation, and reward programs. Education is generally regarded as a necessary and essential requirement for human development. It is central to socioeconomic and technological advancements, and it is critical to the self-generating process of positive transformation in modern society. Education is partially about primary socialization and partly about the process of imparting knowledge for progress and development, both at the individual and group levels. Education is not just about literacy and enlightenment. It is about value formation, value generation, and orientation. Having critically examined the word “study,” what is the perception or attitude of students towards study? This leads us to the meaning and effect of this perception towards study. Attitude or perception, as defined by a researcher, is a mental or neural state of readiness organized through experience exerting a directive or dynamic influence upon the individual response to all subjects and situations with which it is related. In 1996, a researcher defined attitude as a kind of mental state, representing a predisposition to form an opinion. Attitude is one of the determining factors that aid the development of interest, which guides action, and the type of attitude that students have developed towards learning has been directed to a great extent by their academic performance. Thomas (1977) observed that students who have a positive perception of a subject teacher perform better than those who have a negative perception of their subject. There are also some attitudes that can affect students learning and have implications for their performance. These attitudes include students’ expectations, self-concept, cultural differences, and motivation [4]. Sodipo (2015). We enjoin our readers to refer to [10]–[86] of our references. An extension of classical statistics is modern neutrosophic statistics. In classical statistics, the data is known and formed by crisp numbers, while in neutrosophic statistics, the data may have some forms of indeterminacy. Multiple problems, such as attributes in decision-making processes, are often solved using hesitant, fuzzy linguistic information. In the case of the neutrosophic statistics, the data may not be so direct. It may seem vague, ambiguous, incomplete, imprecise, or even unknown.[2] (Florentin Smarandache, 2014). In practice. Sets (such as intervals) [1] in neutrosophic statistics are used instead of crisp numbers in classical statistics. In addition, the neutrosophic concepts are undoubtedly very applicable to a host of important statistical and mathematical ideals and concepts [5, 9]. 2 |Preliminaries Since the advent of neutrosophic statistics through the concerted efforts of Prof. Dr. Florentin Smarandache, many other significant and essential concepts have continually been developed. This includes, among others, the introduction of the Neutrosophic Descriptive Statistics (NDS), the Neutrosophic Inferential Statistics (NIS), the Neutrosophic Applied Statistics (NAS), and the Neutrosophic Statistical Quality Control (NSQC). Neutrosophic statistics is also a generalization of interval statistics. This is because while interval statistics is based on interval analysis, neutrosophic statistics is based on set analysis (meaning all kinds of sets, not only intervals). Hence, the neutrosophic statistics seem to be more elastic when compared with the classical statistics. For instance, if all the data and inference methods are determinate, then the neutrosophic statistics coincide with the classical statistics. In reality, our world possesses more indeterminate data than determinate data. Hence, there is definitely a need for more neutrosophic statistical procedures than classical ones. 9 Adebisi and Broumi | Neutrosophic Opt. Int. Syst. 2 (2024) 7-18 3 |On Neutrosophic Statistics In neutrosophic statistics, the data may be ambiguous, vague, imprecise, incomplete, or even unknown. Instead of crisp numbers used in classical statistics, one uses sets (that respectively approximate these crisp numbers) in neutrosophic statistics [2] (Florentin Smarandache, 2014). Also, in neutrosophic statistics, the sample size may not be exactly known (for example, the sample size could be between 30 and 80; this may happen because, for example, the statistician is not sure about the 50 sample individuals if they belong or not to the population of interest, or because the 50 sample individuals only partially belong to the population of interest while partially they don’t belong) [8]. In this example, the neutrosophic sample size is taken as an interval n = [30, 80], instead of a crisp number n = 30 (or n = 80) as in classical statistics. Neutrosophic statistics refers to a set of data, such that the data or a part of it is indeterminate in some degree, and to methods used to analyze the data (Florentin Smarandache, 2014) [2]. In classical statistics, all data are determined; this is the distinction between neutrosophic statistics and classical statistics. In many cases, when indeterminacy is zero, neutrosophic statistics coincide with classical statistics. We can use the neutrosophic measure for measuring indeterminate data. Neutrosophic data is data that contains some indeterminacy. Similarly to classical statistics, it can be classified as: - discrete neutrosophic data, if the values are isolated points;for example: 6 + 𝑖1, where 𝑖1 ∈[0,1], 7, 26 + 𝑖2, 𝑖2 ∈[3,5]; - and continuous neutrosophic data, if the values form one or more intervals, for example: [0,0.4] or [0.2 ,1.4] (i.e. not sure which one). Another classification: - quantitative (numerical) neutrosophic data; for example: a number in the interval [2, 5] (we do not know exactly), 47, 52, 67 or 69 (we do not know exactly); - and qualitative (categorical) neutrosophic data; for example: blue or red (we don’t know exactly), white, black or green or yellow (not knowing exactly (Florentin Smarandache , 2014 ) [2]. Also, we may have: - univariate neutrosophic data, i.e. neutro-sophic data that consists of observations on a neutrosophic single attribute; and multivariable neutrosophic data, i.e. neutrosophic data that consists of observations on two or more attributes. As a particular cases we mention the bivariate neutrosophic data, and trivariateneutrosophic data. A Neutrosopical Statistical Number N has the form: 𝑁 = 𝑑 + 𝑖, where d is the determinate (sure) part of N, and iis the indeterminate (unsure) part of N. For example, 𝑎 = 5 + 𝑖, where 𝑖∈ [0, 0.4],is equivalent to 𝑎∈ [5, 5.4], so for sure 𝑎 ≥ 5 (meaning that the determinate part of a is 5), while the indeterminate part 𝑖∈ [0,0.4] means the possibility for number “a” to be a little bigger than 5. While the Classical Statistics deals with determinate data and determinate inference methods only, the Neutrosophic Statistics deals with indeterminate data, i.e. data that has some degree of indeterminacy (unclear, vague, partially unknown, contradictory, incomplete, etc.), and indeterminate inference methods that contain degrees of indeterminacy as well (for example, instead of crisparguments and values for the probability distributions, charts, diagrams, algorithms, functions etc. Neutrosophic Numbers of the form N = a+bI have been defined by W.B. Vasantha Kandasamy and F. Smarandache in 2003, and theywere interpreted as "a" is the determinate part of the number N, and "bI"as the ndeterminate. In Imprecise Probability, the probability of an event is a subset T in [0,1], not a number p in [0, 1], what’s left is supposed to be the opposite, subset F (also from the unit interval [0, 1]); there is no indeterminate subset I in imprecise probability ( F. Smarandache, 2013)[3] .The function that models the Neutrosophic Probability of a random variable x is called Neutrosophic distribution: NP(x) = ( T(x), I(x), F(x) ), where T(x) represents the probability that value x occurs, F(x) represents the probability that value x does not occur, and I(x) represents the indeterminate / unknown probability of value x. It could be deduced that the Neutrosophic idea is continuous within the interval while the crisp idea is discrete. And so, combining the cases we have as required and indicated: NP(x) = (T(x), I(x), F(x)). A true neutrosophic number contains the indeterminacy I with a non-zero coefficient. According to M. Mahmud etal (2020) [7], the generalization of the Fuzzy set and Intuitionistic Fuzzy set concept is called as neutrosophic set. This is a powerful general 01 Assessing Students Performance Using Neutrosophic Tool formal framework. The components in neutrosophic set has a degree of truth (T), indeterminacy (I) and falsity (F).The value of this components are between [0,1], respectively. A neutrosphic set has a general formal framework for analysing uncertainty in data set or undetermined information. Not only uncertainty, neutrosophic set can also analyse large information sets or big data sets as well. Single Valued Neutrosophioc sets (SVNs) was introduce to be used expediently to deal with real problems and it is appropriate in solving data mining problem and make a decision for the problem. In their paper, titled “ Student engagement and attitude in mathematics achievement using single valued neutrosophic set “, Single valued neutrosophic set (SVNs) was proposed to measuring factors impact on student engagement and attitude in mathematics achievement based on Trends in International Mathematics and Science Study TIMSS 2015 for ASEAN countries. Although the neutrosophic statistics has been defined since 1996, and published in the 1998 book Neutrosophy/ Neutrosophic Probability, Set, and Logic, it has not been developed since now. A similar fate had the neutrosophic probability that, except a few sporadic articles published in the meantime, it was barely developed in the 2013 book “Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability”. Neutrosophic Statistics is an extension of the classical statistics,and one deals with set values instead of crisp values. Neutrosophic Statistics refers to a set of data, such that the data or a part of it are indeterminate in some degree, and to methods used to analyze the data. In Classical Statistics all data are determined; this is the distinction between neutrosophic statistics and classical statistics. Tables 1 - 5 below show the ( percentage ) performance of some sets of six classes of science students in a particular high school in selected five core subjects for the sciences. Table 1. shows the percentage performance of some sets of six classes of science students in a particular high school in the core subjects: English. Class Students score range JS1 JS2 JS3 SS1 SS2 SS3 39-62 44-61 56–64 54-60 50-63 37-73 Table 2. shows the percentage performance of some sets of six classes of science students in a particular high school in the core subjects: mathematics. Class Students score range JS1 JS2 JS3 SS1 SS2 SS3 54-66 63-67 60-72 58-67 68-76 47-94 Table 3. shows the percentage performance of some sets of six classes of science students in a particular high school in the core subjects: physics. Class Students score range JS1 JS2 JS3 SS1 SS2 SS3 34-50 44-60 53-67 62-73 44–68 37-76 Table 4. shows the percentage performance of some sets of six classes of science students in a particular high school in the core subjects: chemistry. Class Students score range JS1 JS2 JS3 SS1 SS2 SS3 52-67 48-65 45-68 46-68 40–70 36-80 Table 5. shows the percentage performance of some sets of six classes of science students in a particular high school in the core subjects: biology. Class Students score range JS1 JS2 JS3 SS1 SS2 SS3 56-68 48-72 55-67 54-76 45–70 37-92 00 Adebisi and Broumi | Neutrosophic Opt. Int. Syst. 2 (2024) 7-18 4 | Neutrosophic Frequency Distribution A neutrosophic frequency distribution is a table displaying the categories, frequencies, and relative frequencies with some indeterminacies. Most often, indeterminacies occur due to imprecise, incomplete, or unknown data related to frequency. As a consequence, relative frequency becomes imprecise, incomplete, or unknown too. The frequencies are not crisp numbers as in classical statistics, but between some limits. In real life, we cannot always compute or provide exact values for the statistical characteristics, but we need to approximate them. This is one way of passing from classical to neutrosophic statistics. An example of the neutrosophic frequency distribution concerning the range of scores for five core subjects for science students in a certain high school is done subject by subject as follows using Tables 6–10: Table 6. shows the neutrosophic frequency distribution and the neutrosophic relative frequency distribution concerning the range of scores for the science students in a certain high school in the core subject: english. CLASSES Neutrosophic frequency Neutrosophic relative frequency JSS1 JSS2 JSS3 SS1 SS2 [39 , 62] [44 , 61] [56 , 64] [54 , 60] [50 , 63] [ 0.102, 0.221] [0.115, 0.218] [0.146, 0.229] [0.141, 0.214] [0.131, 0.225] SS3 TOTAL : JSS1 – SS3 [37 , 73] [280 , 383] [0.097, 0.261] [ 0.731, 1.368] From here , the minimum neutrosophic frequency for the English classes of scores could be calculated as follows : 𝑀𝑖𝑛nf(e) = 39 + 44 + 56 +54 +50 +37 = 280 and 𝑀𝑎𝑥nf(e) = 62 + 61 + 64 +60 + 63 + 73 = 383 Also, for the neutrosophic relative frequency, we have as follows: The 𝑀𝑖𝑛nf(e) and 𝑀𝑎𝑥nf(e) [39 , 62] ÷ [280 , 383] = [0.102, 0.221] Table 7. shows the neutrosophic frequency distribution and the neutrosophic relative frequency distribution concerning the range of scores for the science students in a certain high school in the core subject: mathematics. CLASSES Neutrosophic frequency Neutrosophic relative frequency JSS1 JSS2 [54 , 66] [63 , 67] [ 0.122, 0.189] [0.142, 0.191] JSS3 SS1 SS2 SS3 TOTAL : JSS1 – SS3 [60 , 72] [58 , 67] [68 , 76] [47, 94] [350 , 442] [0.136, 0.206] [0.131, 0.191] [0.154, 0.217] [0.106, 0.266] [0.791, 1.260] For the JSS1 class , we have the calculations as follows: 𝑀𝑖𝑛nf(e) = 54 + 63 + 60 +58 +68 +47 = 350 and 𝑀𝑎𝑥nf(e) = 66 + 67 + 72 +67 +76 + 94 = 442 Also, for the neutrosophic relative frequency, we have as follows: The 𝑀𝑖𝑛nf(e) and 𝑀𝑎𝑥nf(e) = [54 , 66] ÷ [350 , 442] = [ 0.122, 0.189] 01 Assessing Students Performance Using Neutrosophic Tool Other calculations are thus obtained analogously and recorded in the respective cells of the tables. In order to make our calculations easier, we quickly give the approximate total neutrosophic relative frequencies as recorded in the tables. Table 8. shows the neutrosophic frequency distribution and the neutrosophic relative frequency distribution concerning the range of scores for the science students in a certain high school in the core subject: physics. CLASSES Neutrosophic frequency Neutrosophic relative frequency JSS1 [34 , 50] [44 , 60] [53 , 67] [62 , 73] [44 , 68] [37 , 76] [274 , 394] [0.086, 0.183] [0.117, 0.219] [0.135, 0.245] [0.157, 0.266] [0.112, 0.248] [0.094, 0.277] [0.701, 1.438] JSS2 JSS3 SS1 SS2 SS3 TOTAL : JSS1 – SS3 Table 9. shows the neutrosophic frequency distribution and the neutrosophic relative frequency distribution concerning the range of scores for the science students in a certain high school in the core subject: chemistry. CLASSES Neutrosophic frequency Neutrosophic relative frequency JSS1 JSS2 JSS3 SS1 SS2 SS3 TOTAL : JSS1 – SS3 [52 , 67] [48 , 65] [45 , 68] [46 , 68] [40 , 70] [36 , 80] [267 , 418] [0.124 . 0. 251] [0.115 . 0.244] [0. 108. 0. 255] [0.110 . 0. 255] [0.096 . 0. 262] [0. 086. 0. 300] [0.639 .1.567] Table 10. shows the neutrosophic frequency distribution and the neutrosophic relative frequency distribution concerning the range of scores for the science students in a certain high school in the core subject: biology. CLASSES Neutrosophic frequency JSS1 JSS2 JSS3 SS1 SS2 SS3 TOTAL : JSS1 – SS3 [56 , 68] [48 ,72] [55 , 67] [54 , 76] [45 , 70] [37 , 92] [295 , 445] Neutrosophic relative frequency [0. 126 . 0. 231] [0. 108. 0. 244] [0.124 . 0. 227] [0.121 . 0. 258] [0. 101. 0. 237] [0.083 . 0. 312] [0.663 .1.509] 5 |Classical Statistical Frequency Distribution Another idea for solving this problem would be to transform the neutrosophic data into classical data, either by taking the midpoint of each set or. In classical statistics, all data are determined; this is the distinction between neutrosophic statistics and classical statistics. While classical statistics refers to randomness only, neutrosophic statistics refers to both randomness and especially indeterminacy. While the classical samples provide accurate information, the neutrosophic samples provide vague or incomplete information. Neutrosophic statistics is an extension of classical statistics. While in classical 01 Adebisi and Broumi | Neutrosophic Opt. Int. Syst. 2 (2024) 7-18 statistics the data is known and formed by crisp numbers, in neutrosophic statistics the data has some indeterminacy. In neutrosophic statistics, the data may be ambiguous, vague, imprecise, incomplete, or even unknown. Instead of crisp numbers used in classical statistics, one uses sets (that respectively approximate these crisp numbers) in neutrosophic statistics. In Tables 11–15, the neutrosophic form data has been transformed into a crisp format. This is done by finding the average mean for each subject in the entire set of classes of the students under the assessment. Table 11. shows the neutrosophic form data transformed into a crisp format for the core subject: English. Class Students score range Class average score Total JS1 JS2 JS3 SS1 SS2 SS3 39-62 44-61 56–64 54–60 50-63 37-73 50.5 52.5 60.0 57.0 56.5 55.0 331.5 Average = 331.5 ÷ 6 = 55.25 Table 12. shows the neutrosophic form data transformed into a crisp format for the core subject: mathematics. Class JS1 JS2 JS3 Students score range 54-66 63-67 60-72 Class average score 60 65 66 Total 396 SS1 58-67 SS2 SS3 68-76 47–94 72 70.5 62.5 Average = 396.0 ÷ 6 = 66.00 Table 13. shows the neutrosophic form data transformed into a crisp format for the core subject: physics. Class Students score range Class average score Total JS1 JS2 JS3 SS1 SS2 SS3 34-50 44-60 53-67 62-73 44-68 37–76 42 52 60 67.5 56 56.5 334 Average = 334.0 ÷ 6 = 55.67 Table 14. shows the neutrosophic form data transformed into the crisp format for the core subject: chemistry. Class JS1 JS2 JS3 SS1 SS2 SS3 Students score range 52-67 48-65 45-68 46- 68 40-70 36-80 Class average score 59.5 56.5 56.5 57.0 55.0 58.0 Total 342.5 Average = 342.5 ÷ 6 = 57.10 Table 15. shows the neutrosophic form data transformed into a crisp format for the core subject: biology. Class Students score range Class average score Total JS1 JS2 JS3 SS1 SS2 SS3 56-68 48-72 55-67 54-76 45-70 37-92 62.0 60.0 61.0 65.0 57.5 64.5 Average = 370.0 ÷ 6 = 61.67 Assessing Students Performance Using Neutrosophic Tool 01 6 |Analysis If we are to judge the performances by the highest attainable score for each subject , clearly , it could easily be observed that 1.567 > 1.509 > 1.438 > 1.368 > 1.260, and accordingly, the order of performance from the highest to the lowest can be in this order Chemistry > Biology > Physics > English > Mathematics Going by the classical statistical mean average for each subject for the sets of classes, we have the level of performance represented in the following manner: Mathematics. 1 (66.00 ) > Biology. 2 (61.67) > Chemistry. 3 (57.10 ) > Physics. 4 (55.67 ) > English. 5 ( 55.25 ). 7 |Interpretation From the analysis of the event, the following observations emerge: (i) The classical statistics predict that the students are good in mathematics but very weak in English. (ii). The neutrosophic statistics predict that the students are poor in mathematics but very good in chemistry. If we go by the prediction of classical statistics, one may be deceived to believe that the academic performance of this set of students is okay for their chosen career since their mathematics as a core subject is on good ground. But the prediction of the neutrosophic statistics is very much in order, at least to be on the server side. This is because if one believes that the students performance in mathematics is poor, then efforts would be put in place to improve them and give them more of what it takes to prepare them for further future examinations. 8 |Conclusion The classical statistical analysis may be faulty and not able to supply the required information necessary for the expected demand, whereas the neutrosophic statistics help in providing what could be of advantage for necessary improvements for future expectations. For future research, the authors are proposing the following: (i). Taking care of the other categories of measures of central tendencies involving neutrosophic statistics is also to be considered for the assessment and evaluation of students academic performance and other spheres of performance assessment. (ii). Putting in more of the Multi-Criteria Decision-Making (MCDM) analysis and subsequently the evolving algorithms on the subject. Acknowledgments The author is grateful to the editorial and reviewers, as well as the correspondent author, who offered assistance in the form of advice, assessment, and checking during the study period. Author Contributaion All authors contributed equally to this work. Funding This research has no funding source. Data Availability The datasets generated during and/or analyzed during the current study are not publicly available due to the privacy-preserving nature of the data but are available from the corresponding author upon reasonable request. 01 Adebisi and Broumi | Neutrosophic Opt. Int. Syst. 2 (2024) 7-18 Conflicts of Interest The authors declare that there is no conflict of interest in the research. Ethical Approval This article does not contain any studies with human participants or animals performed by any of the authors. References Huidobro, P., Alonso, P., Jani, V., & Montes, S. (2022). Convexity and level sets for interval-valued fuzzy sets. Fuzzy Optimization and Decision Making, 21(4), 553-580. Florentin Smarandache (2014) introduction to neutrosophic statisticssitech& education publishing F. Smarandache(2013) Introduction to Neutrosophic Measure, Neutrosophic Integral,and Neutrosophic Probability, Sitech Publishing House, Craiova, http://fs.unm.edu/NeutrosophicMeasureIntegralProbability.pdf Sodipo, E. O., Sodipo, A. A. and Adepoju, K. A.( 2015) Statistical analysis of students’ academic performance in nigeria universities: a case study of the University of Ibadan, Nigeria. International Journal of Recent Advances in Multidisciplinary Research Vol. 02, Issue 02, pp.0187-0192 Adebisi Sunday Adesina (2023) Neutrosophic structures in statistical general mathematical functions , Applied Sciences Research Periodicals,vol.1, No 8, pp. 27-32 Haitham I. A. Ward etal ( 2023)Using the Neutrosophic Measurement Technique to Evaluate the Level of Human Resources Performance Journal of Business and Environmental Sciences Volume: 2 (2): Page: 275-302 https://doi.org/10.21608/JCESE.2023.213475.1035 Mahmud M. etal (2020) Student engagement and attitude in mathematicsachievement using single valued neutrosophic set, Journal of Physics: Conference Series 1496 012017 doi:10.1088/1742-6596/1496/1/012017 Vasantha W. B., Kandasamy, Florentin Smarandache, Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps, Xiquan, Phoenix, 211 p., 2003,http://fs.unm.edu/NCMs.pdf https://en.wikipedia.org/wiki/Transcendental_function Sarah A. Alwarthan et al (2022) Predicting Student Academic Performance at Higher Education Using Data Mining: A Systematic ReviewApplied Computational Intelligence and Soft Computing, Article ID 8924028, 26 pages https://doi.org/10.1155/2022/8924028 Elisha Kolluri (2021) Educational measurement and evaluation International Journal of Education, Modern Management, Applied Science & Social Science (IJEMMASSS) ISSN : 2581-9925, Impact Factor: 6.340, Volume 03, No. 04(I), pp.12-20 E. Alyahyan and D. Dusteaor, (2020) “Decision trees for very early prediction of student’s achievement,” 2020 2nd International Conference on Computer and Information Sciences (ICCIS),vol. 2020 N. Alangari and R. Alturki, (2020) Predicting students final GPA using 15 classification algorithms, Romanian Journal of Information Science and Technology, vol. 23, no. 3, pp. 238–249, C. Romero and S. Ventura, (2020) Educational data mining and learning analytics: an updated survey,” WIREs Data Mining and Knowledge Discovery, vol. 10, no. 3, pp. 1–21, H. A. Mengash, (2020) Using data mining techniques to predict student performance to support decision making in university admission systems, IEEE Access, vol. 8, pp. 55462–55470. A. K. Hamoud, A. S. Hashim, and W. A. Awadh, (2018) Predicting student performance in higher education institutions using decision tree analysis,” International Journal of Interactive Multimedia and Artificial Intelligence, vol. 5, no. 2, p. 26, R. Vidhya and G. Vadivu, (2020) Retracted article: towards developing an ensemble based two-level student classification model (ESCM) using advanced learning patterns and analytics, Journal of Ambient Intelligence and Humanized Computing, vol. 12, no. 7, pp. 7095–7105, G. A. S. Santos, et al (2020) Evolved Tree: analyzing student dropout in Universities,” in Proceedings of the 2020 International Conference on Systems, Signals and Image Processing (IWSSIP), Niter´oi, Brazil J. Niyogisubizo, et al (2022) Predicting student’s dropout in university classes using two-layer ensemble machine learning approach: a novel stacked generalization , Computers & Education: Artificial Intelligence, vol. 3, Article ID 100066, F. A. Bello, et al (2020) Using machine learning methods to identify significant variables for the prediction of first-year Informatics Engineering students dropout,” in Proceedings of the 2020 39th International Conference of the Chilean Computer Science Society (SCCC), Coquimbo, Chile,. J. Teguh Santoso, et al (2021) Comparison of classification data mining C4.5 and Na¨ıve Bayes algorithms of EDM dataset, TEM Journal, vol. 10, no. 4, pp. 1738–1744 A. I. Adekitan and O. Salau, (2019) e impact of engineering students’ performance in the first three years on their graduation result using educational data mining,” Heliyon, vol. 5, no. 2, Article ID e01250 Assessing Students Performance Using Neutrosophic Tool 01 P. D. Gil, et al (2021) A data-driven approach to predict first-year students’ academic success in higher education institutions,” Education and Information Technologies, vol. 26, no. 2, pp. 2165–2190 T. Doleck, et al (2020) Predictive analytics in education: a comparison of deep learning frameworks,” Education and Information Technologies, vol. 25, no. 3, pp. 1951–1963. L. Chen, T.-T. Huynh-Cam, and H. Le, (2021) “Using Decision Trees and Random Forest Algorithms to Predict and Determine Factors Contributing to First-Year University Students’ Learning Performance,” Algorithms, vol. 14 H. Zeineddine, U. Braendle, and A. Farah, (2021) Enhancing prediction of student success: automated machine learning approach,” Computers & Electrical Engineering, vol. 89, Article ID 106903. W. Nuankaew and J. 'ongkam, (2020) “Improving student academic performance prediction models using feature selection,” in Proceedings of the 2020 17th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), pp. 392– 395, Phuket, 'ailand. A. I. Adekitan and E. Noma-Osaghae, (2019) “Data mining approach to predicting the performance of first year student in a university using the admission requirements,” Education and Information Technologies, vol. 24, no. 2, pp. 1527–1543 J. Willems, et all (2019) L. Coertjens, B. Tambuyzer, and V. Donche, “Identifying science students at risk in the first year of higher education: the incremental value of non-cognitive variables in predicting early academic achievement,” European Journal of Psychology of Education, vol. 34, no. 4, pp. 847– 872 M. Ya˘gcı, (2022) “Educational data mining: prediction of students’ academic performance using machine learning algorithms,” Smart Learning Environments, vol. 9, no. 1, p. 11,. M. Adnan, (2021) “Predicting At-Risk Students at Different Percentages of Course Length for Early Intervention Using Machine Learning Models,” IEEE Access, vol. 9, pp. 7519– 7539. M. Injadat, et al (2020) Multisplit optimized bagging ensemble model selection for multiclass educational data mining,” Applied Intelligence, vol. 50,no. 12, pp. 4506–4528,. A. Salah et al (2020) Student performance prediction model based on supervised machine learning algorithms,” IOP Conference Series: Materials Science and Engineering, vol. 928, no. 3, Article ID032019 A. Kumar et al (2020) Using early assessment performance as early warning signs to identify at-risk students in programming courses,” in Proceedings of the 2020 IEEE Frontiers in Education Conference (FIE), Uppsala, Sweden,. E. Alyahyan and D. Dusteaor, (2020) “Decision trees for very early prediction of student’s achievement,” 2020 2nd International Conference on Computer and Information Sciences (ICCIS), vol. 2020. N. Alangari and R. Alturki, (2020) “Predicting students final GPA using 15 classification algorithms,” Romanian Journal of Information Science and Technology, vol. 23, no. 3, pp. 238–249, H. Sahlaoui, et al (2021) Predicting and interpreting student performance using ensemble models and shapley additive explanations,” IEEE Access, vol. 9, pp. 152688–152703. Hanushek, E. A. (2020). Education production functions. In S. Bradley & C. Green (Eds.), The economics of education: A comprehensive overview (pp. 161–170). Elsevier Ltd. https://doi.org/10.4337/9781785369070. 00016 Hatane, S. E., Semuel, H., Setiawan, F. F., Setiono, F. J., & Mangoting, Y. (2020). Learning environment, students’ attitude and intention to enhance current knowledge in the context of choosing accounting career. Journal of Applied Research in Higher Education, 13(1), 79–97. https://doi.org/10.1108/ JARHE-06-2019-0156 Ezenwoke, O. A., Efobi, U. R., Asaleye, A. J., & Felix, D. E. (2020). The determinants of undergraduate accounting students’ early participation in professional examinations. Cogent Education, 7(1), 1818411. https://doi.org/10.1080/2331186X.2020. 1818411 Supreme Council of Cultural Revolution (2021). Policies and criteria for organizing assessment and acceptance Applicants for admission to higher education. Resolution no. 3217: avalable at: https://sccr.ir/pro/3217/ Agoestina Mappadang, Khusaini Khusaini, Melan Sinaga & Elizabeth Elizabeth (2022) Academic interest determines the academic performance of undergraduate accounting students: Multinomial logit evidence, Cogent Business & Management, 9:1, 2101326, DOI: 10.1080/23311975.2022.2101326 Soleyman Zolfagharnaasab et al (2023) Equating and Linking Scores in National Exams Educational management and evaluation studies Gyöngyvér Molnár & Ádám Kocsis (2023): Cognitive and noncognitive predictors of academic success in higher education: a large-scale longitudinal study, Studies in Higher Education, DOI: 10.1080/03075079.2023.2271513 Alhadabi, Amal, and Aryn C. Karpinski. 2020. “Grit, Self-Efficacy, Achievement Orientation Goals, and Academic Performance in University Students.” International Journal of Adolescence and Youth 25 (1): 519–35. https://doi. org/10.1080/02673843.2019.1679202. Alyahyan, Eyman, and Dilek Düştegör. 2020. “An Academic Arabic Corpus for Plagiarism Detection: Design, Construction and Experimentation.” International Journal of Educational Technology in Higher Education 17: 1–21. https://doi.org/ 10.1186/s41239-019-0174-x. Azila-Gbettor, Edem M., Christopher Mensah, Martin K. Abiemo, and Marian Bokor. 2021. “Predicting Student Engagement from Self-Efficacy and Autonomous Motivation: A Cross-Sectional Study.” Cogent Education 8 (1): 1942638. https://doi.org/10.1080/2331186X.2021.1942638. Diaz Lema, Melisa, Melvin Vooren, Marta Cannistrà, Chris van Klaveren, Tommaso Agasisti, and Ilja Cornelisz. 2023. “Predicting Dropout in Higher Education Across Borders.” Studies in Higher Education, 1–16. https://doi.org/10. 1080/03075079.2023.2224818. 01 Adebisi and Broumi | Neutrosophic Opt. Int. Syst. 2 (2024) 7-18 Molnár, Gyöngyvér, Saleh Ahmad Alrababah, and Samuel Greiff. 2022. “How we Explore, Interpret, and Solve Complex Problems: A Cross-National Study of Problem-Solving Processes.” Heliyon 8 (1). Molnár, Gyöngyvér, Ágnes Hódi, Éva D. Molnár, Zoltán Nagy, and Benő Csapó. 2021. “Assessment of First-Year University Students: Facilitating an Effective Transition Into Higher Education.” In Új kutatások a neveléstudományokban 2020, edited by Á Engler, and V. Bocsi, 11–26. Debrecen. Molontay, Roland, and Marcell Nagy. 2023. “How to Improve the Predictive Validity of a Composite Admission Score? A Case Study from Hungary.” Assessment & Evaluation in Higher Education 48 (4): 419–37. https://doi.org/10.1080/ 02602938.2022.2093835. Mousa, Mojahed, and Gyöngyvér Molnár. 2020. “Computer-based Training in Math Improves Inductive Reasoning of 9- to 11-Year-old Children.” Thinking Skills and Creativity 37: 100687. https://doi.org/10.1016/j.tsc.2020.100687. Musso, Mariel F., Carlos Felipe Rodríguez Hernández, and Eduardo C. Cascallar. 2020. “Predicting key Educational Outcomes in Academic Trajectories: A Machine-Learning Approach.” Higher Education 80: 875–94. https://doi.org/ 10.1007/s10734-020-00520-7. Rodríguez-Hernández, Carlos Felipe, Eduardo Cascallar, and Eva Kyndt. 2020. “Socio-economic Status and Academic Performance in Higher Education: A Systematic Review.” Educational Research Review 29: 100305. https://doi.org/ 10.1016/j.edurev.2019.100305. Rodríguez-Hernández, Carlos Felipe, Mariel Musso, Eva Kyndt, and Eduardo Cascallar. 2021. “Artificial Neural Networks in Academic Performance Prediction: Systematic Implementation and Predictor Evaluation.” Computers and Education: Artificial Intelligence 2: 100018. https://doi.org/10.1016/j.caeai.2021.100018. Westrick, Paul A., Frank L. Schmidt, Huy Le, Steven B. Robbins, and Justine M. R. Radunzel. 2021. “The Road to Retention Passes Through First Year Academic Performance: A Meta-Analytic Path Analysis of Academic Performance and Persistence.” Educational Assessment 26 (1): 35–51. https://doi.org/10.1080/10627197.2020.1848423. Van Herpen, Sanne G. A., Marieke Meeuwisse, Adriaan W. H. Hofman, and Sabine E. Severiens. 2020. “A Head Start in Higher Education: The Effect of a Transition Intervention on Interaction, Sense of Belonging, and Academic Performance.” Studies in Higher Education 45 (4): 862–77. https://doi.org/10.1080/03075079.2019.1572088. Saumya Kumar Defining And Measuring Academic Performance of Hei Students- A Critical Review Turkish Journal of Computer and Mathematics Education Vol.12 No.6 (2021), 3091-3105 Mansooreh Dastranj (2023) Sociological Explanation of the Factors Affecting the Socio-Cultural Participation of Students of Payame Noor University of BandarAbbas Educational measument and evaluation studies Pintrich, Paul R. (1999). “The Role of Motivation in Promoting and Sustaining Self-Regulated Learning.” InternationalJournal of Educational Research 31 (6): 459–70. https://doi.org/10.1016/S0883-0355(99)00015-4. Ahn, J., & Wang, Y. (2024). The Impact of Leadership on School Organizations: Network Analysis Approach to Systematic Review of Literature on Teaching and Learning International Survey. European Journal of Educational Management, 7(1), 1-17. https://doi.org/10.12973/eujem.7.1.1 Ahn, J., Bowers, A. J., & Welton, A. D. (2021). Leadership for learning as an organization-wide practice: Evidence on its multilevel structure and implications for educational leadership practice and research. International Journal of Leadership in Education. Advance online publication. https://doi.org/10.1080/13603124.2021.1972162 Bernstein, R., Salipante, P., & Weisinger, J. (2021). Performance through diversity and inclusion: Leveraging organizational practices for equity and results. Routledge. https://doi.org/10.4324/9780367822484 Ahn, J., Wang, Y., & Lee, Y. (2023). Interplay between leadership and school-level conditions: A review of literature on the Teaching and Learning International Survey (TALIS). Educational Management Administration & Leadership. Advance online publication. https://doi.org/10.1177/174114322311778 Cann, O. (2020). The reskilling revolution: Better skills, better jobs, better education for a billion people by 2030. World Economic Forum. https://www.weforum.org/press/2020/01/ the-reskilling-revolution-better-skills-better-jobs-bettereducation-for-a-billion-people-by-2030/ Dondi, M., Klier, J., Panier, F., & Schubert, J. (2021). Defining the skills citizens will need in the future world of work. McKinsey Global Institute. Education Design Lab. (2023). The Lab’s 21st Century Skills Micro-credentials. Education Design Lab. https:// eddesignlab.org/microcredentialing/microcredentials/ European Commission Directorate General for Employment, Social Affairs and Inclusion. (2021). ESCO Handbook: European Skills, Competences, Qualifications and Occupations. Government of Singapore. (2022). The Use and Development of Critical Core Skills in Singapore (pp. 96–107). https://www.skillsfuture.gov.sg/-/media/Skills-Report-2022/Final-Files/09-CCS.ashx Freeman, L. C. (1979). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239. https://doi.org/10.1016/0378-8733(78)90021-7 Liu, Y. (2021). Distributed leadership practices and student science performance through the four-path model: examining failure in underprivileged schools. Journal of Educational Administration, 59(4), 472-492. https://doi.org/10.1108/JEA-072020-0159 Wang, Y., & Ahn, J. (2023). The more the merrier? A network analysis of construct content validity in school leadership literature. Educational Management Administration & Leadership. Advance online publication. https://doi.org/10.1177/17411432231155730 Assessing Students Performance Using Neutrosophic Tool 08 Nasser Said Al Husaini (2023)Factors Affecting Students’ Academic Performance Social Science Journal M. Bhutto, Sana Siddiqui, Isma Arain, Qasim Anwar, “Supervised Machine Learning,” Predict. Students’ Acad. Perform. Through Supervised Mach. Learn., 2020, doi: 10.1201/9780429297595. H. A. Mengash et al Using data mining techniques to predict student performance to support decision making in university admission systems,” IEEE Access, vol. 8, pp. 55462–55470, 2020, doi: 10.1109/ACCESS.2020.2981905. Brew, E.A., Nketiah, B. and Koranteng, R. (2021) A Literature Review of Academic Performance, an Insight into Factors and their Influences on Academic Outcomes of Students at Senior High Schools. Open Access Library Journal , 8: e7423. https://doi.org/10.4236/oalib.1107423 Baskerville, D.J. (2020) Mattering; Changing the Narrative in Secondary Schools for Youth Who Truant. Journal of Youth Studies , 23, 1-16. https://doi.org/10.1080/13676261.2020.1772962 O. Gervasi et al. (Eds.): ICCSA 2021, LNCS 12957, pp. 481–491, 2021.https://doi.org/10.1007/978-3-030-87013-3_36 Jayaprakash, S., Krishnan, S., Jaiganesh, V.: Predicting students academic performance using an improved random forest classifier. In: 2020 International Conference on Emerging Smart Computing and Informatics (ESCI), Pune, India, pp. 238– 243, March 2020. https://doi.org/ 10.1109/ESCI48226.2020.9167547 Bhutto, E.S., Siddiqui, I.F., Arain, Q.A., (2020) Anwar, M.: Predicting students’ academic performance through supervised machine learning. In: 2020 International Conference on Information Science and Communication Technology (ICISCT), Karachi, Pakistan, pp. 1–6, https://doi.org/10.1109/ICISCT49550.2020.9080033 Al Mayahi,K., Al-Bahri,M. (2020): Machine learning based predicting student academic success. In: 2020 12th International Congress onUltraModern Telecommunications and Control Systems andWorkshops (ICUMT), Brno, Czech Republic, pp. 264–268, https://doi.org/ 10.1109/ICUMT51630.2020.9222435 H. Waheed, S. U. Hassan, N. R. Aljohani, J. Hardman, S. Alelyani, and R. Nawaz, “Predicting academic performance of students from VLE big data using deep learning models,” Comput. Human Behav., vol. 104, 2020, doi: 10.1016/j.chb.2019.106189. Yousuf Nasser Said Al Husaini et al Prediction methods on students’ academic performance: Jilin Daxue Xuebao (Gongxueban)/Journal of Jilin University (Engineering and Technology Edition) ISSN：1671-5497 E-Publication Online Open Access Vol: 41 Issue: 09-2022 DOI 10.17605/OSF.IO/CHJF2 Shah Hussain et al Student Performulator: Predicting Students’ Academic Performance at Secondary and Intermediate Level Using Machine Learning Annals of Data Science (2023) 10(3):637–655. https://doi.org/10.1007/s40745-021-00341-0 Google Scholar. (n.d.). Top publications in educational administration. Retrieved December 1, 2020, from https://bit.ly/4c9zVYK Alturki et al. (2022) Predicting Master’s students’ academic performance: an empirical study in Germany Smart Learning Environments (2022) 9:38 https://doi.org/10.1186/s40561-022-00220-y