Charting new territories: fuzzy systems in English language teaching and learning

Motivation

Communicating effectively in English is more important in today’s globalized society, yet secondary school curricula only sometimes meet students’ needs. Traditional approaches emphasize translation and terminology but downplay the importance of listening and speaking as communication skills. The Fuzzy Bayesian Intelligent Tutoring System (FB-ITS) provides adaptive learning environments tailored to each student to compensate for these limitations. When dealing with ambiguous data, FB-ITS improves the accuracy of student and instructor performance evaluations by using fuzzy logic and Bayesian networks. Evidence of its efficacy includes more precise assessments and better use of available resources, which bode well for the future of English language education.

Problem statement

Underprepared students, especially for college and beyond, are an expected outcome of the conventional wisdom on English language instruction in secondary schools. Listening and speaking should be addressed in favor of systems emphasizing translation, rote memorization of words, and vocabulary. Also, when dealing with ambiguous or inaccurate data, traditional assessment methods need help understanding how well both students and instructors are doing. This results in an imbalance between efficient instruction methods and student progress evaluation. Improving English proficiency is vital in today’s globalized and linked society. Thus, there is an urgent need for adaptable, intelligent solutions that can tackle these issues.

Novelty

By incorporating new fuzzy membership functions developed for linguistic mistake categorization, this article improves the present FB-ITS system and allows more accurate handling of ambiguity in student answers. Learning recommendations are updated continuously based on real-time error analysis. The system includes an efficient Bayesian inference process. The construction of a hybrid fuzzy Bayesian model is a significant technological contribution. This model incorporates weighted parameters to alter the recommendation approach depending on learner advancement and categorizes mistakes into granular levels, such as lexical, grammatical, and syntactic. According to experimental findings, the suggested approach is a vast improvement over current intelligent tutoring systems, showing that adaptive exercise creation, error correction accuracy, and overall learning efficiency are significantly improved.

This article’s main contributions are

• This work proposed an AI-based system that changes to fit each student’s requirements

• The proposed model formulates a fuzzy logic framework with improved English instruction approach for student’s achievement with more individualized learning environment that can boost productivity and interest.

• The proposed system considerably decreases students’ time on learning assignments while enhancing resource utilization.

The remaining section of this article is structured as follows: In “Related Work”, the related work of the language teaching system is studied. In “Proposed Method”, the proposed methodology of FB-ITS is explained. In “Result and Discussion”, the efficiency of FB-ITS is discussed and analysed. Finally, in “Conclusion”, the article concludes with future work.

Fuzzy system for language learning apps

The impact of particular combinations of variables on this intention has yet to be largely overlooked. With this research, we want to shed light on the factors influencing students’ frequent intentions to use a tool: cognitive need, subjective norms, perceived utility, satisfaction, confirmation, attitude, and perceived ease of use. Core factors strengthening learners’ continuing intention were identified as learners’ happiness with MLA use and cognitive requirement and attitude by Hossain et al. (2021).

Fuzzy-Felder-Silverman model

According to Troussas et al. (2020), this process is difficult and time-consuming, which leads to students’ questionnaires being randomly selected. This approach in turn, leads to incorrect adaptation to their requirements and puts their knowledge acquisition at risk. In addition, limited mobile user interfaces make it hard to pick questionnaire options in mobile contexts. This study introduces Learnglish, a fully functional mobile language learning system that automatically uses ensemble classification to identify students’ learning styles based on fuzzy-Felder-Silverman model (F-FSM).

Artificial intelligence-based fuzzy system for pronunciation

Sound quality, timbre, pitch strength, voice, and breathing stability are all technical characteristics of a singer’s singing that may be objectively evaluated to determine how well they pronounce words. Each human voice has unique physical characteristics in terms of pitch, volume, timbre, and sound quality. Studies in this area have shown that a high-quality singing voice’s frequency and energy spectra vary significantly from those of a low-quality singing voice. Tang, Gao & Ouyang (2023) try to build an AI-based assessment model of singing pronunciation quality.

Deep learning based fuzzy technology

Some of the most significant obstacles remain in system implementation, language adaptability, and performance robustness. Although it is one of the world’s most spoken languages, Hindi is also one of the most challenging and resource-constrained languages. Therefore, to disseminate technology and discover new ways of communicating, systems for voice recognition and classification must be created for the English language by Sharma, Om & Mishra (2023). However, developing such systems is relatively rigid owing to the language’s complexity compared to other languages and the absence of shared databases.

Fuzzy computing based on big data

First, it employs sparse word-sense expressions of mixed semantics via nonnegative matrix decomposition of positive point mutual information between words and contexts. To begin, it extracts the low-rank expressions of the mixed semantics of the polysemous words using the nonnegative matrix decomposition of the positive pointwise mutual information between words and contexts by Liu & Tsai (2021). Then, it uses the sparse soft clustering algorithm to partition the multiple-word senses of the polysemous words and obtains the global sense of the polysemous word affiliation distribution.

Educational data mining in fuzzy network

Charitopoulos, Rangoussi & Koulouriotis (2020) goal is to provide a literature review of current studies that have used Soft Computing techniques to analyze educational data “mined” from interactive/e-learning systems to solve challenges linked to education. Such systems are renowned for producing and storing massive amounts of data that may be used to evaluate the learner, the system, and the efficacy of their interaction. Two separate but related fields of study, educational data mining (EDM) and learning analytics (LA), use this data to answer unanswered questions or solve problems in education.

Machine learning approach for universal language

Twitter sentiment detectors outperform more conventional methods of gauging product and service quality. They employ high-quality input features and rely on TSDs’ classification accuracy and detection performance, which are highly dependent on the success of the classification algorithms.

According to AlBadani, Shi & Dong (2022), automating workflow processing is difficult for all firms since current machine learning algorithms require high processing time.

Support vector machine in language analysis

Most themed databases use statistical approaches like the keyword matching method for information. However, this approach can’t determine how people feel about articles; it only works for retrieving those with the exact or related subject keywords. In addition, everyone agrees that there are situations when theme material cannot be sought using keywords alone. Despite categorizing it into related themes, (Han et al., 2020) categorise its emotional stances as neutral or contradictory.

Annamalai, Uthayakumaran & Zyoud (2023) suggested augmented reality and virtual reality (AR-VR) for English language teaching and learning activities. The results showed that people had good and bad opinions about using AR and VR in ESL classrooms. The positive themes were active learning, bringing your device (BYOD), student engagement, and successful English language acquisition. Things that were seen as time-consuming and health-related were associated with unfavorable views. The research proposed methods that may work when incorporating AR and VR into ESL classrooms. The current study aims to shed light on the pros and downsides of augmented and virtual reality technology so that educators, curriculum developers, and policymakers may weigh these factors before incorporating them into English language classrooms.

Zhi & Wang (2023) introduced the structural equation modeling (SEM) approach for English as a foreign language teachers’ professional success, loving pedagogy, and creativity. The effects of four dimensions of educators’ inventiveness on the connection between caring pedagogy and their career advancement were examined using mediation analysis. In conclusion, language-teaching stakeholders in the EFL context have been provided with some suggestions on how to stimulate EFL teacher training programs that lead to the success of both instructors and students. One such suggestion is to boost the growth of educational research on diverse topics.

Voreopoulou, Mystakidis & Tsinakos (2024) discussed the augmented reality escape classroom game for deep and meaningful English language learning. A 33-item survey and semi-structured interviews were used to gather information. The results indicate that this escape game may be an excellent tool for teaching English as a second language since it can help students become more culturally aware, improve their vocabulary recall, and improve their ability to listen to and understand spoken English. The game’s humorous and interactive aspects encourage students to actively communicate, collaborate, be creative, think critically, and work in groups. This model creates a cheerful environment that helps students stay motivated and satisfied while learning a new language. This research offers recommendations and backing for creating comparable augmented reality escape classroom games (ARECGs) to enhance teaching methods and language instruction.

Hu & Luo (2024) presented the neuro/metacognitive and socio-cultural strategies for vocabulary retention for Chinese English language learners. The experimental and control groups, which consisted of 90 EFL learners from educational institutions in China in 2022 and 2023, used a quasi-experimental pre-test/post-test design. Throughout eight sessions, 45 students in the experimental group were taught using mind mapping, visual imagery, multisensory rotation, and circle rotation techniques; 45 students in the control group were taught using more conventional approaches. Results from statistical analyses using SPSS version 22’s variance and covariance analysis showed that the experimental and control groups improved recall and word recognition significantly.

This study focuses on fuzzy systems and artificial intelligence methods for language analysis and learning. Students’ intentions to use mobile language applications are influenced by cognitive demand, contentment, and perceived ease of use, which the Fuzzy system for language learning apps (FS-LLA) investigates in Table 1. Improve the mobile app experience with the help of the F-FSM. One area of emphasis for artificial intelligence-based fuzzy system for pronunciation (AI-FS-P) is evaluating voice quality using AI-based pronunciation tests. While fuzzy computing based on big data (FC-BD) uses big data for semantic analysis, deep learning based fuzzy technology (DL-FT) faces difficulties building language recognition systems. Regarding educational data analysis, educational data mining in fuzzy network (EDM-FN) and support vector machine in language analysis (SVM-LA) are used for linguistic datasets that deal with emotional analysis.

Contribution 1: development of FB-ITS

The FB-ITS system is an advanced ERRS or educational resource referral system, and its purpose is to give students suggestions for individualized educational resources. It generates personalized recommendations based on data collected from user actions, including login, browsing, searching, and downloading. User and resource modeling are essential components that contribute to a recommendation system that guarantees students get educational resources that are appropriate to their needs.

A thorough framework for the ITS that incorporates many cutting-edge technologies to improve education. Students can access the system’s personalised feedback and suggestions via the user interface, which is fundamental to its operation. The feedback & recommendation module keeps these insights up-to-date so that student progress may be followed continually. The student model and the adaptation module are essential parts that come together to provide personalized English learning experiences. The student model captures learner profiles, results, and habits. The adaptation module, meanwhile, makes use of this information to tailor the lesson to each learner. The knowledge base compiles relevant educational and subject-matter resources to aid with adaptation. The Bayesian inference and fuzzy logic engine form the backbone of these modules; they collaborate to handle uncertainty, make probabilistic judgments, and deliver correct, context-sensitive suggestions. This clever combination of reasoning and inference provides a responsive and flexible English learning environment, as shown in Fig. 1.

(1) $$w\ge Q\left(b+\right)=G_f\ast MO\left(V_r-2r\right)-\left(W_q-3f\right).$$Fuzzy logic’s contribution to guiding is represented by the Eq. (1) $G_f$. Qb+ denotes student motivation, and performance metrics $W_q-3f$ and resource factors are related to the variables $w$ and $MO$. The goal of this equation is to measure the system’s effect on student learning efficiency, with an emphasis on harmony.

(2) $$\mathrm{\forall }\ast \mathrm{E}\mathrm{Y}\left({\mathrm{z}}^{\mathrm{\prime }}-\mathrm{b}\mathrm{v}\right)=\mathrm{Y}{n}^{2-q}\ast DA\left(v^2-w\right).$$The system is dynamically adjusted according to student engagement $\mathrm{\forall }$ and performance measures, as indicated by the equation $\mathrm{Y}{n}^{2-q}$, and the predicted yield of learning $DA\left(v^2-w\right)$ outcomes are captured by Eq. (2), $\mathrm{E}\mathrm{Y}\left({\mathrm{z}}^{\mathrm{\prime }}-\mathrm{b}\mathrm{v}\right)$. By demonstrating the direct relationship between changes system response and overall learning effectiveness, the equation seeks to bolster the adaptive character of the FB-ITS.

(3) $$b^{\mathrm{\prime }\mathrm{\prime }}=c\left(Z_1,A\left(d-fp\right)\right)\ast J{k}^{n-2q}+Ez\left(\mathrm{\partial }-2w\right).$$With $Z_1,A\left(d-fp\right)$ denoting the impact of contextual variables $J{k}^{n-2q}$ and individual student characteristics $Ez\left(\mathrm{\partial }-2w\right)$ on learning results, the Eq. (3), $b^{\mathrm{\prime }\mathrm{\prime }}$ depicts the revised efficiency of the tutoring system. This equation highlights the significance of constant FB-ITS modification based on real-time input and ambient factors.

(4) $$c_1=\left(y_2,\mathrm{\forall }\left(Z_{d-2v}\ast E\left(m\ast n^2+Rz\right)\right)\right).$$Factoring in the interaction between numerous students $m\ast n^2$ and the responsiveness of the system $Rz$, Eq. (4), $c_1$ encompasses the combined contributions of several aspects $\mathrm{\forall }$, such as student engagement $y_2$ and overall adaptability $Z_{d-2v}\ast E$. This equation aims to demonstrate a tailored learning environment by incorporating varied inputs and experiences, improving English learning results.

(5) $$V_b=D\left(m{g}^{n-2v}\ast \mathrm{m}\mathrm{a}\mathrm{x}\mathrm{w}\left(r^{2}sd-2vq\right)\right).$$The system’s value boost is represented by the Eq. (5) $V_b$, where $D$ is a dynamic component that includes motivation $r^{2}sd$ and pupil involvement $m{g}^{n-2v}$ is the influence of resource allocation $2vq$ on the efficacy of English learning $\mathrm{m}\mathrm{a}\mathrm{x}$. To maximize the educational achievements by the FB-ITS approach, this equation stresses the significance of engaging students to their fullest potential.

A system for referring students to relevant educational resources that uses data on their actions to provide tailored suggestions. Important user activities contributing to the user behaviour data are highlighted at the top. These actions include login, resource browsing, searching, evaluation, and downloading, as shown in Fig. 2. The system’s suggestion mechanism is built upon this data. Essential to the central portion are the models for users and resources. Individual users are profiled via the user modelling component according to their preferences and interactions. At the same time, the resource modelling part arranges instructional materials in a way that meets the user’s requirements. Taking the two models as inputs, the recommendation algorithm combines both models to filter and retrieve information about the user. Several operational modules have been put in place to support the system. Resource management assures that a high level of quality resources is available while user management supports user activities. The systems also help prevent abuse of the services by employing system maintenance, although additional filtering rules are used to narrow the scope of the presented suggestions. System administration ensures that the management is at the center of the system, governance provision, and well-functioning and meeting users’ expectations.

(6) $$w\ge e\left(b{n}^2-gf\right)=Y^{nv}-Er\left(m^2\ast Qw\right).$$Equation (6) $w$ captures the $m^2\ast Qw$ between baseline performance $e$ and parameters like pupil input and resource allocation $Y^{nv}$, whereas $b{n}^2-gf$ reflects the minimal effectiveness $Er$ of the English tutoring system. This equation highlights the requirement to overcome a performance threshold to guarantee that the FB-ITS promotes enhanced language competence among students.

(7) $$E_4=\left(Y_w\ast 2p\right)\ast (w{q}_2-Rf\left(v-bz\right).$$The total efficacy $Rf$ of teaching tactics $v-bz$ is denoted by the equation $E_4$, where $Y_w$ represents student engagement levels, and $2p$ represents the quality of feedback $w{q}_2$. With Eq. (7), individualized learning demonstrates how adaptive English teaching approaches and student motivation work together to maximize English learning results.

(8) $$Wn\left(E^2-bq\right)=a\ast n{b}^2\left(de-vf\ast m{a}^3\right).$$Equation E2-bq emphasizes effective English teaching approaches $Wn$ and student involvement $de-vf$, while equation $\left(8\right)$, A*nb2, represents the weight of the educational advantages $m{a}^3$ obtained from the system. Equation (8) shows that the method promotes better language proficiency via a flexible and organized educational framework by balancing the quality of teaching.

As stated in the previous sections, the primary activities of the system and supporting activities of resource management, user management, and system maintenance ensure the system’s operation efficiently and effectively. Employing Bayesian Inference for the reasoning process along with fuzzy logic, we can offer the most suitable idea, which is continually altered to meet the individual requirements of the wanting learner. Hence,adaptive learning, which is flexible and customized, is created.

Contribution 2: implementation of the proposed method

The need for individual educational intervention that meets students’ cognitive and communicative needs has led the developers to incorporate fuzzy logic and expand its boundaries. This approach allows using student data and feedback to adapt both assessment criteria and the English teaching materials in different inference engines working in parallel. These capabilities enable FB-ITS to handle students’ unclear responses and reasonably speculate about the learning patterns and the related probabilities.

An outline for a method of teaching English that enhances students’ language abilities via integrating several components. Developing fluency in speaking, reading, and writing is the central objective of the English teaching goal. This method incorporates a variety of instructional resources, including a mix of three-dimensional English learning materials designed for use in both traditional classroom settings and more modern online ones. Students gain more from online self-study and guidance than from teacher-facilitated Interpretation of teaching in more conventional classrooms. The English teaching organiser and teachers are essential in content structure and delivery. Ensuring that classes are well-organized and that teaching tactics align with the aims is the responsibility of the teaching contents, management, and methods. Students can actively participate in the content via various instructional tactics, promoting thorough language learning, and this system’s flexible teaching strategy, which combines self-paced and teacher-guided methods, is shown in Fig. 3.

(9) $$q<g\left(b\left(Z_1,M_3\left(Q{v}^2-kl\right)\right)\right)+E\left(n^2-wq\right).$$The minimal anticipated quality $E\left(n^2-wq\right)$ of learning results is represented by the Eq. (9), $q<g$, and the system’s capacity $Q{v}^2-kl$ to boost student engagement is denoted by $Z_1,M_3$. This equation highlights the importance of FB-ITS meeting a certain quality standard, guaranteeing instructional techniques.

(10) $$Z_2=\left(y_2,\mathrm{\forall }\left(Z-2\right)\right)\ast Q_r=\left(m_2,\phi \left(\rho \sigma -\pi \right)\right).$$Equation (10) $Z_2$ represents the interplay of several elements $\mathrm{\forall }$ impacting English learning outcomes $y_2$, including motivation $Q_r$ and contextual variables $m_2$, whereas equation $\mathrm{\forall }\left(Z-2\right)$ captures students’ total engagement $\phi \left(\rho \sigma -\pi \right)$ and performance levels. The equation highlights the need to regularly evaluate and modify instructional approaches to cultivate a more customized and adaptable learning environment.

(11) $$\mathrm{\forall }\left(w{f}^2-mk\right)=b^{\mathrm{\prime }}\ast \left(M{n}_2-Qw\left(e{v}^2-r\right)\right).$$The total student involvement $\mathrm{\forall }$ and resource utilization $b^{\mathrm{\prime }}$ are represented by the Eq. (11) $w{f}^2-mk$, while the efficiency $Qw$ of adaptive learning $e{v}^2-r$ techniques are shown by $M{n}_2$. For educational results to be instructional approaches to connect student input with system responsiveness, as shown by this Eq. (11).

(12) $$r>p\left(k\right),m\left(w-q\right)=B\left(e+2n\right)-\left(Wr-2p\right).$$The desired performance $r$ level is represented by the Eq. (12) $m\left(w-q\right)$, and the alignment $Wr-2p$ of student involvement $B\left(e+2n\right)$ with the instructional quality shown by $p\left(k\right)$. As the equation shows, educational practices must go above and beyond to succeed.

FB-ITS is an AI system that uses Bayesian networks and fuzzy logic to create unique lessons for each student. An outline of the method of teaching English which incorporates some components and enables its students to improve their language skills. It involves allowing the students to talk, read, and compose, thus making them fluent in communicating in English by focusing on the English teaching goal: comprehension. This method includes adding learning materials as three-dimensional interactive resources that can be used in conventional face-to-face and contemporary e-learning.

Data and student feedback is the first stage within the AI system, considering the decision-making process. The Bayesian inference engine and the fuzzy inference engine collaborate to achieve this, as illustrated in Fig. 4, capture the student’s lesson plans and measure their performance. The instruction incorporating fuzzy logic accommodates the vagueness and imprecision of each student’s response and works toward preparing the respective material. Precisely, Bayesian inference helps in understanding the behavioral aspects of students, such as the possible correlation of specific actions to academic achievements.

Clustering algorithms utilize these results to adjust the instructional material to the needs of a specific individual student. That brings out the need for an adaptive feedback system within the system to help the teachers and the learners optimize the learning strategies employed. Achievement of English learning outcomes, such as increased language proficiency and swifter exam completion, is developed through AI techniques by FB-ITS, which brings a more flexible, efficient, and data-oriented approach to teaching. Consequently, individualized education is provided to each child.

(13) $$\omega \left(r^{\mathrm{\prime }}Bj-Ew\left(e^r-aq\right)\right)=\beta \left(\gamma -\delta \epsilon \right)+\mathrm{Z}.$$ $Ew$ (student outcomes) and $r^{\mathrm{\prime }}Bj$ (resource effectiveness) are using a weighting factor $\omega$ in the equation er-aq. Improving the quality of instruction $\beta \left(\gamma -\delta \epsilon \right)$ and student engagement Z are both emphasized. This Eq. (13), shows that adaptive teaching tactics interact with student performance measurements.

(14) $$E=\mathrm{\forall }\left\{M\left(Q-w{r}^{\mathrm{\prime }}\right)\right\}+E-Pj\left(n^2-wk\right).$$The total educational effectiveness is represented by the Eq. (14) $M\left(Q-w{r}^{\mathrm{\prime }}\right)$, which $\mathrm{\forall }$ means the balance $E-Pj$ between English learning quality $\left(n^2-wk\right)$ and student engagement and $E$ reflects the influence of adaptive feedback $E$. Improving language proficiency with adaptive learning technology requires a holistic strategy since this equation emphasizes the complex character.

Regarding clustering algorithms, FB-ITS restructures its pedagogical approach and offers Adaptive Feedback to teachers and learners. Constantly adjusting teaching methods during class to meet each learner’s particular needs is an effective and flexible way of improving educational achievements such as test performance and skills. It offers a highly efficient and data-led English learning ecosystem.

Contribution 3: evaluation of the proposed method using a mathematical equation

The three main parts of this English learning framework before, in, and after class are all meant to help students succeed. Students are adequately prepared for class because of the system’s emphasis on self-learning and instructor supervision in the days leading up to it. Cooperative learning strategies that encourage participation and the exchange of information are the mainstay of classroom instruction. Figure 5 shows the diagram of students’ English learning classes.

A method for studying the English language that is organized into three distinct stages: pre-class, during-class, and post-class. Students work on their core knowledge via self-learning in the before-class phase, either with the help of instructors or on their own. During the in-class portion of the learning process, students work together in small groups to complete assigned tasks. As part of performance measurement, two main activities involve sampling inspection and stage detection, wherein students’ English learning accrual is evaluated. Other vital technologies are scene, evaluation, and group communication, which are directed toward supporting students in collaborative learning, sharing ideas, and expanding the concept. In the after-class phase, students improve their comprehension through teacher tutoring and expanded knowledge. This assists in reinforcing the subject of the class while advocating supportive practical training even when the students are finished with formal education. This all-around approach is illustrated to provide students with the optimal result in terms of English learning outcomes: individual study, group work in the classroom, and reinforcement after class.

(15) $$B_1\le k\left(b-mn\right)\ast N_3=df\left(c_1,z_f,bq\right).$$The quality of instruction $c_1,z_f,bq$, and student involvement $B_1$ impact the efficacy of learning $N_3$, as shown by the Eq. (15) $k\left(b-mn\right)$, which is a standard for educational results $df$. The function captures the dynamic aspects impacting these measures, highlighting the need to integrate multiple components to guarantee that educational plans meet.

(16) $$c\le d\left(b_2\right)=Z\left(f-2w\right)+\left(E^{2}Q\left(n^{\mathrm{\prime }}q\right)\right).$$db2 shows a function that considers instructional quality and student interaction $\mathrm{a}\mathrm{s}\mathrm{i}\mathrm{n}$ Eq. (16) $c$ reflects the permissible limit for educational results. Optimizing language acquisition requires methods brought to light by the expressions $Z\left(f-2w\right)$ and $E^{2}Q\left(n^{\mathrm{\prime }}q\right)$. Equation (16) emphasizes the importance of adaptive feedback and the use of resources for English learning effectiveness in the analysis of learning efficiency.

(17) $$R\left(c-b\right)=F\left(N^2+Ew\right)+H\left(c^2-Jp\right).$$Equation (17) $R\left(c-b\right)$ is denoted as the necessary enhancement in performance, where $F\left(N^2+Ew\right)$ represents the combined impact of pupil involvement. The effect of adaptive teaching methods is summed up by the expression $H\left(c^2-Jp\right)$. This Eq. (18) highlights resources and strategies to accomplish specific English learning objectives to analysis of optimized resource utilization.

(18) $$-p^{\mathrm{\prime }\mathrm{\prime }}\left(y-x^{\mathrm{\prime }}\right)=nr\left(v-wq\right)+C\left(n-bv\right).$$The effect of instructional changes $nr$ on student performance is shown by the Eq. (18) $—p^{″}\left(y-x^{\mathrm{\prime }}\right)$, At the same time, the influence of resource allocation $C\left(n-bv\right)$ and level of engagement is demonstrated by $v-wq$. This Eq. (18) highlights the need to constantly adjust English teaching methods to maximise student involvement and competence in addressing uncertainty.

(19) $$R_{a}tW=\left\{\left(b,dr\right)\ast M^{2}Q:e-{\displaystyle \frac{2}{6}}\right\}\ast E-r^{\mathrm{\prime }}p\ast 2b.$$The total efficiency of resource allocation $E-r^{\mathrm{\prime }}p\ast 2b$ is represented by the Eq. (19) $R_{a}tW$, and the contributions $e-{\displaystyle \frac{2}{6}}$ of instructional quality $M^{2}Q$ and student engagement are captured by $\left(b,dr\right)$. This equation emphasizes improving learning effectiveness and student competency in language acquisition when analyzing academic performance.

(20) $${\mathrm{\partial }}_{3}Q\left(k^{\mathrm{\prime }}-hp\right)=\sin H\left(Y;z-1\left(n-2k{b}^{\mathrm{\prime }}\right)\right).$$The rate of change $\mathrm{s}\mathrm{i}\mathrm{n}$ in learning outcomes $n-2k{b}^{\mathrm{\prime }}$ impacted by important instructional variables $H$ is represented by the Eq. (19) ${\mathrm{\partial }}_{3}Q\left(k^{\mathrm{\prime }}-hp\right)$, and Y shows the interplay of several contextual aspects impacting engagement $;z-1$. This Eq. (20) highlights the ever-changing nature of students’ unique English learning demands, therefore greatly influencing their success in the analysis of assessment accuracy.

Through analysis of performance and the recommendation of individualized exercises, the FB-ITS dynamically adjusts to a student’s advancement. For example, suppose a learner has difficulties with prepositions. In that case, the system employs fuzzy logic to categorize mistakes as either “minor” (such as a mix-up between “in” and “on”) or “major” (such as improper application in intricate phrases). “He arrived___the station,” for example, and the Bayesian module suggests targeted fill-in-the-blank exercises as a means of development, with feedback elaborating on the difference between being “at” a specific location and being “in” within a place. The correct response is “at.” To provide a consistently tailored and efficient learning experience, the system upgrades the complexity and suggests more sophisticated assignments as the student progresses.

Moreover, it has been seen that students who need assistance use, for instance, tutoring and many activities offered after class to reinforce the material learned in class. In other words, this framework which emphasizes the self and culminates in measures to include classroom and post-class learning, leads to a well-rounded approach that enhances English language skills, motivates participation, and assures students of better understanding.

Dataset description

Mastering the art of writing is essential. Unfortunately, few pupils can improve this skill because writing assignments are rare in the classroom. English language learners, a rapidly expanding student group, are particularly impacted by the need for more practice. Although automatic feedback technologies let instructors provide more writing assignments, they must be suited for English language learners. The current technologies cannot consider the student’s language skills while providing feedback, which means that the final assessment might be biased against the student. Data science might enhance automated feedback technologies to cater to these students’ requirements (Dutta, 2022; Ezhilmathi et al., 2024). The performance of the suggested FB-ITS model has been analyzed based on metrics such as learning efficiency, assessment accuracy, optimized resource utilization, uncertainty addressing, and academic performance compared to existing methods FS-LLA (Hossain et al., 2021), F-FSM (Troussas et al., 2020), AI-FS-P (Tang, Gao & Ouyang, 2023), DL-FT (Sharma, Om & Mishra, 2023), and FC-BD (Liu & Tsai, 2021).

Analysis of learning efficiency

Particularly in the context of English language instruction, state-of-the-art AI systems such as the FB-ITS show considerable improvements in learning efficacy. Traditional methods emphasizing copying, memorization, and text analysis are ineffective in improving language competence. FB-ITS considers each student’s unique learning requirements and assessment uncertainties using artificial intelligence approaches like Bayesian networks and fuzzy logic to provide adaptive assistance as explained in Eq. (16). The results of the experiments show that compared to students using traditional e-learning techniques, students utilizing FB-ITS finish tasks faster and take less time to do the post-tests. The system’s clustering techniques for extensive data also boost assessment accuracy by 4% and enhance the utilisation of teaching resources by 5%. These findings highlight the promise of AI-powered solutions to transform language acquisition by creating a data-driven, more individualized learning environment that boosts productivity and interest. Learning efficiency is improved by 98.86%, as shown in Fig. 6.

Analysis of assessment accuracy

Assessments in educational contexts, especially language acquisition, have been made more accurate with AI-driven systems such as the FB-ITS. The complexity of students’ learning development cannot be adequately captured by traditional assessment systems that depend on numerical scores, mainly when dealing with subjective or inaccurate information, which is explained in Eq. (17). By combining fuzzy logic with Bayesian networks, FB-ITS can handle uncertainty and adapt to individual learning demands, resulting in a more nuanced assessment. The FB-ITS outperformed traditional systems by 4% in evaluation accuracy in experimental investigations. The system’s capacity to analyze massive amounts of data, classify students’ learning behaviors, and provide customized feedback is the root cause of this enhancement. Oversized data clustering methods enhance the evaluation process, guaranteeing it captures a more comprehensive picture of the student’s skills. Evaluating students’ performance is now fairer and more precise than using this novel technique. In Fig. 7, the assessment accuracy is increased by 97.13% in the proposed method of FB-ITS.

Analysis of optimized resource utilization

Especially in ESL classrooms, the FB-ITS has increased efficiency in using available resources. Inefficient use of teaching resources is a common problem with traditional methods since they can’t adjust material delivery according to individual learning progress. FB-ITS uses artificial intelligence techniques like Bayesian networks and fuzzy logic to adapt lesson plans and content on the fly based on individual student’s strengths and weaknesses, as explained in Eq. (18). This adaptive technique guarantees that educational resources are allocated more efficiently. To minimize the time and effort wasted by students and teachers, the system delivers tailored activities to decrease duplication. The experiment results demonstrate that, compared to the traditional approaches, the utilization of instructional resources is 5% higher. In addition to making instructional material distribution more efficient, this enhancement promotes a more streamlined and effective learning environment by allowing resources to be adjusted to maximize educational results while minimizing expense. The optimized resource utilization is obtained by 96.51%, as shown in Fig. 8

Analysis of addressing uncertainty

In Fig. 9, FB-ITS also meets one of the requisites of teaching with contemporary educational technology by addressing the issue of uncertainty. In such conventional assessment systems, the degree of difficulty in evaluating students’ achievement is exacerbated by the fact that they rely on arbitrary and rigid numbers, which often do not capture the broad scope of learning achieved. Constructed to incorporate the nonlinear features of the system, education environments that are diverse by utilizing fuzzy logic together with Bayesian networks are resolved by FB-ITS in a high-tech manner. As a result of the system’s ability to accept imprecise or missing information, more accurate and complete evaluations can be made. In addressing the limitations of vague data, it uses fuzzy logic and Bayesian networks to update the previous learning assessments with recent information. This style ensures that there is a healthy alteration of system responses to individual learner demands while at the same time enhancing understanding of the student’s growth. FB-ITS ensures a balanced and impartial evaluation of learning results through appropriate ambiguity avoidance. The addressing uncertainty is gained by 97.36% in the proposed method of FB-ITS using Eq. (19).

Analysis of academic performance

The development of the fuzzy Bayesian intelligent tutoring system and other advanced artificial systems has made the academic achievement process much more accessible. In some cases, standardized tests and marking systems utilized to determine academic performance may fail to capture the intricacies or evolution of the learners over time. FB-ITS shifts the deficiencies of the relatively rigid methods laid out in the previous systems by adapting to new environments and learning differences and eliminating ambiguity through fuzzy logic and Bayesian networks, which implies a broader evaluation is contained in Eq. 20. The system further well captures the actual potential of the individual students because of its ability to manage and process large amounts of educational information. It incorporates wet efficiency and instruction based on examinations; it factors participation and comprehension as efficiency indices. The experimental results have found that FB-ITS increases the accuracy of the evaluation of the academic results by 4%, which indicates a provision of more profound and more credible measures of the learners’ performance in Table 2. This method provides teachers with a clear understanding of achievement and practices that need to be improved to encourage more effective teaching methods. The improvement in academic performance illustrates this by 99.25%, shown in Fig. 10.

A thorough comparative study assessed the accuracy, flexibility, and learning efficiency of the proposed FB-ITS model compared to other intelligent tutoring systems. By reducing reaction time for adaptive exercise creation by 20% and improving error classification accuracy by 15%, FB-ITS surpasses conventional models such as rule-based systems and simple Bayesian networks. Compared to baseline systems, the fuzzy-Bayesian hybrid model had a 25% higher learner advancement rate, demonstrating improved flexibility. Pairwise t-tests were used to verify statistical significance, which confirms that the suggested method is robust. Experiments using separate experimental and control groups yielded the claimed gains in assessment accuracy (4% improvement) and instructional resource utilization rate (5% improvement). One hundred students participated in the study using the suggested FB-ITS model, whereas one hundred students in the control group used more conventional rule-based tutoring methods. Both groups were a perfect fit regarding age, level of language competence, and learning goals. Over 12 weeks, participants were asked to complete a battery of standardized tests and activities. Extensive records of system interactions, precision in exercise completion, and access to instructional resources were used to compute the measures. To confirm the findings and ensure the improvements were reliable and statistically significant, paired t-tests and other analyses were conducted.

In summary, FB-ITS has significantly enhanced several areas of English language training. Its adaptive and data-driven approaches improve resource utilization, speed up work completion, and increase assessment accuracy. Assessments are now more precise and tailored to each student’s needs, as are the system’s sophisticated risk management and nuanced evaluation of academic achievement. These developments demonstrate how AI can revolutionize education by making classrooms more interactive and productive.

Limitations

The quantity and quality of the training data are the primary determinants of the system’s performance. Low or biased datasets could make the system less flexible in adapting to different learning situations, which might result in incorrect predictions or suggestions. For another, it could be challenging to execute in real-time or with limited resources when fuzzy logic and Bayesian inference are combined because of the computational complexity this might bring. Third, the system may have trouble learning languages with subtle nuances or context-specific mistakes since these situations often demand human judgment, which is hard to simulate computationally.

Future work

To further evaluate the efficacy of FB-ITS, future research should concentrate on increasing its use across multiple educational environments. Adding AI approaches like deep learning and natural language processing is worth considering to make the system more versatile and accurate. To further improve the system’s functionality and usability, it is essential to examine user input from students and instructors. Research that follows participants over time can determine how FB-ITS influences their English language skills and academic achievement in the long run. Finally, to make the most of it, it will be essential to create scalable models that can be used in other English languages and educational contexts.