Toward Effective Educational Supervision in Yemen: A Hybrid Fuzzy Delphi and Clustering Analysis of Technical Barriers

1. Introduction

The current global shifts in science and education have significantly impacted various educational dimensions, including systems and supervision processes. These transformations have compelled educators to critically examine educational structures and reaffirm the teacher’s role as a central pillar within the system.¹ Within this context, educational supervision has emerged as a pivotal component of educational management, fundamental to the broader educational framework that encompasses both teaching and learning.² Educational supervision serves as a cornerstone for ensuring educational quality and promoting continuous improvement. It plays a vital role in enhancing teacher performance by offering professional guidance, fostering reflective practice, and aligning teaching with curriculum standards.³ Historically limited to classroom observation, the scope of supervision has expanded to include mentorship, collaborative problem-solving, and the development of targeted professional growth plans.⁴

In today’s dynamic educational landscape—shaped by digital transformation and evolving pedagogical expectations—supervisors are instrumental in helping educators integrate technology, maintain digital ethics, and implement innovative teaching strategies suited to 21st-century learners.⁵ Beyond instructional support, effective supervision also nurtures teachers’ emotional well-being and professional development, ensuring that education remains inclusive, adaptive, and student-centered.⁶ Modern supervisory models now emphasize collaborative learning environments and constructive feedback mechanisms, thereby cultivating a culture of continuous improvement.⁷ As Okafor et al. note, effective supervision not only enhances instructional practices but also strengthens institutional effectiveness by fostering an environment conducive to both teacher and student success.⁸ Given its multifaceted nature, educational supervision continues to evolve—requiring ongoing research and innovation to meet the complex demands of contemporary education.

The success of educational supervision hinges on several critical indicators. Supervisors must offer clear directives and align instructional practices with institutional objectives.⁹ Emphasis should be placed on implementing quality assurance mechanisms that align with global standards while addressing local educational contexts.⁹ Continuous professional development is essential in fostering a culture that supports quality teaching and lifelong learning.^10,11

Moreover, supervision becomes most effective when teachers actively engage with feedback, thereby promoting a culture of accountability and improvement.¹² Effective planning is equally important—supervisors must ensure that their approach is strategic, goal-oriented, and systematic.^13,14 Competent supervisors are characterized by strong instructional leadership, effective communication, accurate observation, and constructive feedback delivery.^15,16 Building trust-based professional relationships between supervisors and teachers further enhances collaboration and facilitates open communication.^17,18 Additionally, the integration of modern technology and the availability of financial and learning resources significantly contribute to the success of supervision practices.¹⁹ These factors collectively support a dynamic, responsive, and impactful supervision system.

Ultimately, educational supervision focuses on actively involving teachers in the learning environment to enhance teaching methods and improve student achievement. It plays a central role in overseeing the educational process by integrating instructional activities and continuously evaluating institutional outcomes.^2,20 Through identifying challenges and working collaboratively to resolve them, supervision ensures the implementation of appropriate actions that drive educational advancement.

Numerous studies indicate that educational supervision, in its current state, faces significant challenges that hinder its effectiveness. Including inadequate training programs,¹⁰ limited planning,²¹ weak supervisory competencies,¹⁵ low teacher acceptance of modern methods,²² strained relationships,¹⁸ technological gaps,¹⁹ and insufficient financial, infrastructural, and learning resources.^2,23 To overcome these barriers, studies recommend structured professional development, strategic planning, competence-based supervisor selection,¹⁶ fostering collaborative cultures,²⁴ integrating digital tools,²⁵ securing adequate funding,²⁶ and providing supportive environments to strengthen supervision’s impact.

Comprehensive educational supervision is a fundamental approach employed in schools to assess and respond to their challenges, needs, and educational and social realities. It involves the continuous presence of educational supervisors within school environments to gain firsthand insights into the teaching and learning processes both inside and outside the classroom. Through this approach, supervisors are able to diagnose the real conditions of the educational system—including the roles of teachers, learners, school leadership, and the broader learning environment. However, in Yemen, the ability to implement effective supervision has been severely undermined by ongoing conflict and political instability. The education system, which once showed progress with enrollment rates increasing from 71.3% to 97.5% between 1999 and 2013, has since experienced significant setbacks. By the 2015/2016 academic year, around 1.8 million children were out of school, and over 1,100 schools had been either destroyed or repurposed for emergency use.²⁷ These structural disruptions have weakened the foundation of educational supervision. Furthermore, the quality of education has declined significantly, with reports of curriculum manipulation for ideological purposes and widespread issues such as the absence of teacher training and salary payments.²⁸ In response to these profound challenges, Yemen’s National Vision for Building the Modern Yemeni State and the national research priorities emphasize the urgent need for comprehensive education reform.

In line with these priorities, this study aims to analyze the technical challenges facing educational supervision in schools located in Amanat Al Asimah and explore viable strategies to improve the efficiency of educational processes. The focus is on supporting national goals by modernizing supervisory practices and ensuring they contribute meaningfully to sustainable development and institutional capacity building. The study seeks to identify, rank, and cluster these challenges in schools within Amanat Al Asimah, Yemen, while exploring viable strategies to enhance the efficiency of educational supervision processes.

The significance of this study lies in its alignment with Yemen’s National Vision for Building a Modern Yemeni State and national research priorities. It contributes to modernizing supervisory practices in a conflict-affected context, supports sustainable development, and enhances institutional capacity in Yemen’s education sector. Additionally, it provides insights into addressing teacher-related challenges and improving the quality of education.

Methodologically, the study employs a mixed-methods approach that includes a literature review to identify key barriers to effective supervision, the Fuzzy Delphi Method to validate and prioritize these barriers, a quantitative survey of teachers to assess their perceptions of supervisory challenges, and fuzzy set theory and K-means clustering analysis to categorize and prioritize the identified barriers.

The findings of this study could inform targeted policy interventions to enhance supervisory effectiveness, guide resource allocation for improving educational supervision, support capacity-building initiatives for supervisors, and contribute to developing a responsive supervision framework aligned with national development objectives.

2. Methods

Multi-Criteria Decision-Making (MCDM) methods have emerged as vital analytical tools in a wide range of fields, including health, sustainability, tourism, healthcare, engineering, education and financial risk assessment.^29–39 The integration of MCDM methods with fuzzy logic and clustering techniques provides a robust framework for addressing complex decisions under uncertainty.^29–33 Fuzzy-based MCDM approaches effectively capture expert ambiguity and contextual nuances, making them particularly suitable for fields such as health, education, and sustainability.^35,38–40 The Fuzzy Delphi Method (FDM), enhanced by fuzzy set theory, improves expert consensus and facilitates clearer selection and prioritization of variables.^35,38,41,42

Meanwhile, machine learning (ML) has significantly advanced real-world decision-making through predictive modeling, risk analysis, and pattern recognition.^43–48 Its applications span various domains, including healthcare,⁴³ big data analytics,⁴⁴ manufacturing quality control,⁴⁵ and infrastructure forecasting.⁴⁶ ML also supports academic evaluation through web mining⁴⁷ and Industry 4.0 applications.⁴⁸

Recent research increasingly integrates MCDM, fuzzy logic, and unsupervised ML techniques—particularly K-means clustering—to enhance decision-making by segmenting barriers and identifying strategic priorities.^29–33 This hybrid approach has been successfully applied in health security,^29–33 ecotourism,³⁹ urban resilience assessment,⁴⁹ and education,^40,50 offering scalable, context-sensitive solutions to complex policy and planning challenges.

Building on these methodological advancements and empirical applications, the present study adopts a similar integrative approach to explore and prioritize barriers in the context of educational supervision in Yemen.

In the present study, the Fuzzy Delphi Method (FDM) was employed as a preliminary phase to identify and validate the most contextually relevant barriers to effective educational supervision in Yemen. The primary purpose of the FDM was not to evaluate or resolve the barriers but to systematically screen and refine a set of candidate variables based on expert consensus for use in subsequent analyses. This was followed by a quantitative teacher survey assessing perceptions of supervisory challenges and the application of fuzzy set theory and K-means clustering to categorize and prioritize the identified barriers. Our analysis was conducted through a structured, three-phase process, with each stage clearly outlined and supported by a rationale for the chosen methodology.

2.3 Barrier prioritization in educational supervision via fuzzy set theory and cluster segmentation

To investigate the technical barriers impacting comprehensive educational supervision in schools in Sana’a, Yemen, a structured questionnaire was developed. The items in this instrument were derived from key barriers previously identified and validated through the Fuzzy Delphi Method. The questionnaire aimed to capture teachers’ perceptions of the supervisory challenges within their institutional contexts.

Step 1: Sample of the Study

A descriptive quantitative approach was employed, aligning with the study’s objective to assess systemic supervisory barriers from the teachers’ perspective. The study population comprised approximately 7,000 teachers working in schools that implemented comprehensive educational supervision in the capital city. Following Krejcie and Morgan’s sampling guidelines, a sample of 370 teachers was selected, surpassing the recommended minimum of 364 for a population of this size. This sample size ensured representativeness and allowed for statistical generalization to the broader population.

Step 2: Research Instrument Design

To gather the necessary data, a structured questionnaire was designed based on the study objectives, relevant literature, validated prior instruments, and the Fuzzy Delphi procedures outlined in Section 2.2. The instrument consisted of 11 items, each corresponding to a specific technical barrier affecting the effectiveness of comprehensive educational supervision. A five-point Likert scale was used to measure participants’ perceptions of each barrier, with response options ranging from “Very Low” (1 point) to “Very High” (5 points). The full scale included very low (1), low (2), moderate (3), high (4), and very high (5).

This structure enabled respondents to express their views clearly and allowed for the consistent quantification of data for analysis.

Step 3: Data Collection Procedures

The questionnaire was distributed across four educational districts in Amanat Al-asima Sana’a, where comprehensive educational supervision is currently being practiced. These districts were selected from among the ten official educational zones in the city of Amanat Al-Asima, Yemen.

Teachers from private schools that implemented comprehensive supervision practices were also included. Completed questionnaires were collected through school administrations and returned directly to the researcher.

Step 4: Aggregation and Defuzzification of Responses

The collected responses were converted into fuzzy numbers using the predefined scale (see Table 1), enabling the representation of uncertainty in respondents’ judgments. The average fuzzy rating for each barrier was calculated across all respondents using Equation 1. These fuzzy values were then defuzzified into crisp scores using the centroid (center of gravity) method, as described in Equation 2 (see Table 6).

Table 6. Respondents’ scores using a fuzzy rating scale.

Respondent No	B1			B2			… .	B11
	m1	m2	m3	m1	m2	m3	… .	m1	m2	m3
R1	0	0	0.2	0.6	0.6	1	… .	0	0.2	0.4
R2	0	0.2	0.4	0	0.6	0.4	… .	0	0.2	0.4
R3	0.6	0.8	1	0.6	0.8	1	… .	0.2	0.4	0.6
R4	0.2	0.4	0.6	0.2	0.4	0.6	… .	0	0	0.2
R5	0	0	0.2	0.4	0.4	0.8	… .	0	0	0.2
R6	0.4	0.6	0.8	0	0.2	0.4	… .	0.4	0.6	0.8
R7	0.2	0.4	0.6	0.4	0.4	0.8	… .	0.6	0.8	1
R8	0.4	0.6	0.8	0.4	0.4	0.8	… .	0.4	0.6	0.8
R9	0.2	0.4	0.6	0.2	0.4	0.6	… .	0.2	0.4	0.6
R10	0.2	0.4	0.6	0.2	0.6	0.6	… .	0.2	0.4	0.6
R11	0.2	0.4	0.6	0.2	0.4	0.6	… .	0.4	0.6	0.8
R12	0.4	0.6	0.8	0.4	0.4	0.8	… .	0.4	0.6	0.8
R13	0	0	0.2	0	0	0.2	… .	0	0	0.2
… ..	… ..	… ..	… ..	… ..	… ..	… ..	… ..	… ..	… ..	… ..
R369	0.4	0.6	0.8	0.4	0.2	0.8	… .	0.4	0.6	0.8
R370	0.6	0.8	1	0.6	0.6	1	… .	0.6	0.8	1
AFR	0.235	0.415	0.615	0.257	0.421	0.648	… .	0.256	0.426	0.626
CS	0.422			0.442			… .	0.436

Following the evaluation of the barriers and the computation of the average score for each based on respondents’ input, the aggregated scores were used to rank and categorize the barriers according to their impact on the effectiveness of comprehensive educational supervision.

Step 5. Clustering Analysis and Barrier Prioritization Using K-Means

The aim of the clustering process was to categorize the identified barriers into distinct groups based on their combined impact. This approach allows for a deeper understanding of the relative effects of these factors on the success of comprehensive educational supervision and enables the targeted prioritization of interventions. Clustering is a fundamental unsupervised machine learning technique that organizes unlabeled data into distinct clusters based on inherent similarities, such as proximity or density metrics.^29–32

Unlike supervised learning, which relies on labeled outputs for training, clustering reveals hidden patterns without predefined categories, making it essential for exploratory analysis. By uncovering latent structures, clustering aids in hypothesis generation and provides valuable insights into strategic decision-making.⁶⁶ Among the various clustering techniques, K-means is particularly favored for its simplicity, computational efficiency, and versatility across disciplines.^29,30

The algorithm partitions n data points into k clusters by minimizing the variance within each cluster. It follows an iterative process^29–33: (1) randomly initializing k centroids; (2) assigning each data point to the nearest centroid; (3) recalculating centroids based on updated cluster memberships; and (4) repeating these steps until the model converges or reaches a predetermined iteration limit.

To determine the optimal number of clusters, the Elbow Method was employed using the Total Sum of Squared Errors (SSE) as a performance metric (see Figure 1). The SSE was computed for k values ranging from one to five. A significant reduction in SSE was observed between k = 1 (0.0055724) and k = 3 (0.0006534), indicating an improved model fit. Beyond k = 3, further reductions in SSE were minimal, suggesting diminishing returns. The inflection point at k = 3, known as the “elbow,” indicates an optimal balance between simplicity and explanatory power. Consequently, k = 3 was selected as the ideal number of clusters.

Figure 1. Elbow Method results for determining the optimal number of clusters.

The plot illustrates the correlation between the within-cluster sum of squares (WCSS) and the number of clusters (k).

The final clustering model classified the barriers into a three-tier system based on their aggregated impacts. Segment 3 represents a high-priority danger zone, encompassing barriers with high average ratings from respondents, indicating significant concerns and severity. Segment 2 reflects a moderate level of concern, where the perceived impact of the barriers is notable but less critical. Segment 1 comprises low-priority or minimal-risk barriers, characterized by relatively low average ratings and limited influence on the effectiveness of comprehensive education supervision. This structured grouping enhances the interpretability of the results and provides a practical framework for prioritizing interventions and developing targeted policy responses.

3. Results

4. Discussion

The Fuzzy Delphi Method (FDM) process confirmed the appropriateness and relevance of all 11 barriers to effective educational supervision. Each barrier met the necessary consensus and threshold criteria, demonstrating that the selected variables were not only theoretically grounded in the literature but also validated by expert opinion as reflective of the real-world challenges facing Yemen’s supervision system.

The high level of consensus among experts (average agreement of 90%) and a low domain-level threshold (0.093) indicate a consistent and strong agreement across the expert panel. These outcomes enhance the methodological rigor and credibility of barrier selection processes. Notably, the high crisp scores obtained for several barriers, particularly those related to resource limitations (e.g., insufficient learning materials and inadequate financial support), highlight their practical significance. These challenges are not just perceived concerns but are deeply embedded in the operational dynamics of the educational supervision system. Even barriers with relatively lower average ratings, such as the lack of training halls or dedicated office space, were retained in the final model, emphasizing their contextual importance despite being perceived as less urgent issues. The use of FDM in this study served as an effective filtering and validation mechanism, ensuring that only the most contextually relevant and expert-validated barriers were included in subsequent analytical phases. This is especially critical in complex decision-making environments, where aligning empirical evidence with expert insights enhances the focus, reliability, and applicability of advanced evaluation models, such as MCDM techniques or policy simulations. By incorporating expert judgment under conditions of uncertainty and applying structured fuzzy logic principles, the method strengthens the foundation for deeper investigation and prioritization [39,42,65].

Following FDM validation, ranking and clustering analyses ( Tables 9 and 10) provided further insights into how these barriers vary in severity and impact. Segmentation into three groups enabled the strategic categorization of challenges, offering a clearer roadmap for targeted interventions and policy reform.

The analysis identified a critical barrier in educational supervision: the weak competencies of educational supervisors (B4). This barrier, despite representing only 9.1% of total concerns, received the highest average score (0.467) and ranked first among all barriers, emphasizing its importance. Consistent with the existing literature,^67–69 this finding highlights the vital role of competent supervision in teacher development, instructional improvement, and overall school enhancement. Competent supervisors possess essential skills in instructional leadership, communication, observation, feedback delivery, and the ability to analyze teaching practices and design appropriate interventions.^15,16 Weak supervisory competencies can undermine the entire supervisory process, leading to unclear guidance, ineffective support, and hindered teacher development,⁷⁰ potentially compromising educational quality and impeding systemic improvement. This analysis emphasizes the need for immediate and sustained action to enhance supervisory competencies, as they form the foundation of effective educational supervision and improve teaching and learning outcomes.^16–18 To address this critical issue, policymakers and educational institutions must prioritize comprehensive professional development programs for supervisors, focusing on continuous training, mentorship programs, tailored performance evaluation systems, and the development of instructional leadership capabilities.^{15,17,18,68,69} Strengthening supervisory competencies is likely to have far-reaching effects, potentially mitigating the interconnected barriers within the educational system.

Furthermore, segment 2, comprising seven barriers and representing the largest portion (63.6%), included various moderate-impact issues influencing daily supervision operations. The most significant barrier, B2: Limited capability in creating effective supervisory plans (average score: 0.442), highlights the necessity of enhanced strategic planning skills among supervisors. This aligns with the understanding that well-developed supervisory plans are essential for effective supervision, providing structure, clear goals, and direction.^53,54 Effective supervisory plans ensure a systematic rather than a reactive process, aligning supervision with instructional improvement. These plans must be goal-oriented, realistic, adaptable, time-bound, and developed collaboratively with the teachers. The ability to create and implement strong supervisory plans is central to ensuring purposeful and focused supervision aligned with educational goals.^13,14 Conversely, poorly planned supervision can be inconsistent or unclear, limiting its impact on teacher development and student learning. Equally concerning is B6: Poor relationships between supervisors and teachers (0.440), which points to underlying communication and trust issues. Effective supervision relies not only on technical competence but also on interpersonal relationships that foster a supportive and collaborative school environment. A professional relationship built on trust and communication encourages teacher openness, responsiveness to feedback, and collaboration.^18,59

In contrast, weak relationships or lack of trust may result in resistance and reduce the impact of supervisory efforts. Additional barriers in this segment include B11: Lack of dedicated offices for educational supervision (0.436) and B3: Limited capability in implementing training programs (0.425). These barriers indicate both infrastructural deficiencies and limited pedagogical leadership, suggesting a need for resource investment and capacity building. Well-designed and timely training programs directly enhance teachers’ instructional skills, promote consistency in instructional quality, and foster a culture of professional growth.^10,11 The distribution of barriers in Segment 2 underscores the need for a comprehensive improvement strategy that addresses both relational and structural challenges. Enhancing supervisors’ abilities across three key dimensions—planning, relational engagement, and training delivery—is foundational to improving the overall effectiveness of supervision systems.

This approach would involve the socioeconomic status: Strengthening planning capabilities to improve the quality, consistency, and outcomes of the educational supervision process; developing meaningful relationships between supervisors and teachers to create a supportive and collaborative environment is essential; improving the design and implementation of impactful training programs to enhance teacher performance and professional development is crucial.

By addressing these interconnected aspects, supervisors can provide more meaningful feedback, manage their time effectively, and identify key areas for improvement.¹³ This comprehensive approach would significantly enhance the quality and impact of educational supervision, ultimately benefiting the development of teachers and student learning outcomes.

Finally, segment 1, comprising three barriers and representing 27.3% of the total, included concerns that were considered low-priority or minimal risk. These barriers are marked by relatively low average ratings and limited impact on the effectiveness of comprehensive educational supervision. Despite being rated as lower priority, the barriers in Segment 1 highlight structural limitations that could negatively affect the supervision process if not addressed. For example, limited teacher acceptance of modern supervisory methods can stifle innovation and diminish the effectiveness of such interventions. When teachers resist collaborative evaluation, peer feedback, or data-informed coaching, it undermines the culture of trust and continuous improvement that is essential for effective supervision.²² Similarly, inadequate financial allocations for supervision activities restrict supervisors’ ability to conduct school visits, attend professional development programs, or acquire necessary materials, resulting in poorly planned and under-resourced supervision systems.^8,23 Additionally, the lack of access to modern technologies limits the use of digital tools for classroom observation, feedback, training and communication. Without these tools, supervision becomes less interactive, data-informed, and responsive.^19,60 While these barriers may not have the most immediate impact, their cumulative effect over time can impede broader reform efforts, stifle innovation, and exacerbate other challenges in educational supervision. Therefore, continuous monitoring and proactive mitigation of lower-ranked issues are crucial for sustaining long-term improvements.

The low average ratings and limited influence of these barriers indicate that resources and efforts should primarily focus on addressing more critical issues in comprehensive educational supervision. Nevertheless, it remains important to monitor these low-priority barriers, as they could potentially affect the overall effectiveness of supervision if neglected for an extended period.

In summary, the integrated FDM and clustering analysis offered a multilayered understanding of the barriers hindering educational supervision in Yemen. The findings emphasize the urgency of enhancing supervisory competencies and highlight the need to address moderate-impact barriers related to planning, relationships, infrastructure, and training. Low-priority issues should not be ignored, as their future impact may become more significant in a changing educational landscape. Collectively, these insights provide a strategic framework for policymakers, educational leaders, and stakeholders to allocate resources, design interventions, and improve supervisory effectiveness, ultimately contributing to more robust and equitable educational outcomes

5. Conclusion

This study systematically investigated the technical barriers undermining the effectiveness of comprehensive educational supervision in Amanat Al Asimah, Yemen, using a robust mixed-methods framework. Eleven key challenges were identified, validated through the Fuzzy Delphi Method, and prioritized using fuzzy set theory and K-means clustering. The Fuzzy Delphi results demonstrated strong expert consensus, with a domain-level threshold of 0.093 and an average agreement of 90%, affirming the contextual relevance of the selected barriers. Through clustering analysis, the barriers were segmented into three priority levels. Segment 3, comprising a single high-priority issue—weak supervisory competencies—emerged as the most critical concern, underscoring the central role of professional capacity in enabling effective supervision. Segment 2 contained seven moderate-priority barriers, including planning deficiencies, strained supervisor–teacher relationships, and inadequate training infrastructure. Segment 1 grouped three low-priority barriers, such as resistance to modern supervision methods and technological or financial constraints, which, though less urgent, could accumulate into significant challenges if left unaddressed.

These findings carry important implications for policymakers, educational leaders, and planners operating in fragile and resource-limited contexts. The study offers a data-driven roadmap for prioritizing reforms, emphasizing the urgent need to invest in supervisory training, institutional planning, and resource allocation. The segmentation of barriers provides a practical framework for designing targeted, phased interventions. Additionally, the approach used in this study can be replicated or adapted to other conflict-affected or low-income settings, contributing to broader efforts in educational reform and capacity building.

However, the study also faces several limitations. It was geographically restricted to Amanat Al Asimah, potentially limiting generalizability across Yemen’s diverse regions. Furthermore, it focused primarily on teachers’ and supervisors’ perspectives, excluding voices from students, principals, and policymakers. Also, it concentrated on technical barriers, leaving out sociopolitical or cultural dimensions that may influence supervisory effectiveness. Future research should expand geographically, incorporate multiple stakeholders, and explore non-technical factors influencing educational supervision. Longitudinal and experimental designs could also evaluate how barriers evolve and how proposed solutions perform over time. Comparative studies across similar contexts could provide valuable benchmarks and inform regional or global supervisory strategies.

In summary, this study highlights the urgency of strengthening supervisory competencies and institutional frameworks to enhance the quality and effectiveness of educational supervision in Yemen. By integrating expert validation, teacher feedback, and advanced clustering techniques, it presents a scalable and evidence-based framework that can inform strategic planning, policy development, and educational resilience in post-crisis and low-resource environments

Ethics and consent

This study adhered to the principles of the Declaration of Helsinki and the national guidelines for research involving human participants. Official permission to conduct the study was secured from the Office of Education, Bani-Alhareth, Amanat Al Asimah, Republic of Yemen (Approval Reference No.: [72-9-24), authorizing data collection from participating schools. Participants received clear information about the study’s objectives and procedures and were assured that their participation was entirely voluntary, with the right to withdraw at any time, without consequences. Written informed consent was obtained from all participants before data collection, and no minors were included in this study.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the author(s) used [DeepSeek v3, Paperpal, Quillbot, and ChatGPT] for language refinement and structure. After using this tools, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.