Decision-oriented assessment of telecom infrastructure for strengthening online education systems Free

Telecom infrastructure is crucial for increasing the accessibility and cost of online education, particularly in underdeveloped nations where conventional educational institutions confront significant structural obstacles. The rapid digital transition has profoundly altered the global academic scene recently. Online education has evolved as a scalable, inclusive and flexible alternative to conventional classroom learning, further driven by global shocks like the COVID-19 pandemic. In this changing educational framework, telecommunications infrastructure is essential, providing the fundamental connection and technical support required for virtual learning experiences. Telecom networks deliver remote education to underprivileged and geographically isolated communities by providing the underlying connection for digital learning. This infrastructure connects students to educational materials by providing dependable internet connectivity and digital platforms required for learning (Romiszowski, 2013). Initiatives like Brazil's Ceará State Digital Belt Project demonstrate national efforts to achieve digital inclusion, to connect more than 80% of the population to broadband connections, allowing for widespread access to online education. Similarly, in some African and Asian nations, government and private sector collaborations strive to provide internet-enabled computers to public schools and community centers, democratizing access to digital instructional material (Mahenge & Mwangoka, 2014). Furthermore, developing cost-effective network topologies for e-learning may dramatically decrease bandwidth utilization and operating expenses, improving the affordability and scalability of education systems (Williams & Eyo, 2011).

Telecom infrastructure also helps reduce online learning costs by enabling mobile-based learning platforms and low-bandwidth alternatives. For example, mobile learning systems may synchronize material for offline access, saving bandwidth and decreasing server demand during peak hours (Mahenge & Mwangoka, 2014). Mobile-based education innovations promote various educational techniques while reducing costs associated with physical infrastructure and classroom upkeep (Suresh Kumar, Hemawathi, Dhanasekaran, Kumar Kaliappan, & Sivaganesan, 2024). Furthermore, low-cost virtual classrooms that function in low-bandwidth contexts provide real-time audio-visual interaction without costly streaming infrastructure, hence increasing access to excellent education even in bandwidth-constrained areas (Mondal, Misra, & Misra, 2013).

In the Indian context, where geographic and socio-economic disparities present considerable obstacles to educational access, telecommunications services' availability, reliability and affordability are essential factors influencing the success of online learning. The recent decade has seen a substantial digital shift, with increasing telecom coverage in rural regions. The growing availability of low-cost cell phones and data subscriptions has allowed millions of students to engage in digital learning, a trend that has grown significantly since the COVID-19 epidemic. Telecom infrastructure includes various technologies and services, such as broadband networks, mobile connectivity (3G, 4G and 5G), cloud services, communication platforms and data analytics tools, collectively enhancing content delivery, student engagement and administrative efficiency in online education systems. Nonetheless, despite its significance, the function of telecom infrastructure has not been carefully examined to ascertain which individual elements most effectively enhance the effectiveness of online learning systems. Although Customer Relationship Management (CRM) software is often used for lead generation in education, it frequently fails to achieve quality conversion due to inefficiencies and insufficient integration with telecommunications capabilities. Utilizing telecom infrastructure for data gathering, outreach and communication offers a cost-efficient means to enhance targeting precision and conversion effectiveness (Suresh Kumar et al., 2024).

Due to telecom infrastructure's intricate and multifaceted characteristics, a comprehensive multi-criteria decision-making (MCDM) methodology is essential for assessing its critical functions in facilitating online education. This research employs a hybrid Fuzzy AHP–Fuzzy VIKOR architecture to bridge this gap, allowing for the integration of expert assessments amid ambiguity and prioritizing numerous criteria. This study, informed by a comprehensive literature review and expert panel discussions, delineates 24 essential roles of telecom infrastructure, classified into eight functional domains: Accessibility & Reach, Communication & Engagement, Content Delivery, Data Analytics & Personalization, Learner Support & Assessment, Cost Efficiency, Security & Reliability and Marketing & Lead Conversion. These roles are evaluated via six principal analytical parameters: Impact on Learning Outcomes, Cost-Effectiveness, Reach and Accessibility, Learner Engagement and Interaction, Reliability and Scalability and Conversion and Outcome Efficiency. Fuzzy logic addresses the ambiguity in human assessments, while the VIKOR technique offers a framework for ranking and picking the best-performing roles under online education. The key goals of this study are:

1. To identify and classify the essential functions of telecommunications infrastructure in online education

2. To ascertain the significance of different evaluation criteria of online education employing Fuzzy AHP

3. Assess and prioritize the key functions based on expert feedback, utilizing the Fuzzy VIKOR method.

4. A sensitivity analysis was performed to evaluate the stability and robustness of the proposed ranking.

This study's findings are anticipated to offer practical insights for policymakers, telecom service providers, ed-tech companies and educational institutions, facilitating the strategic allocation of telecom resources to enhance the effectiveness of online education systems, particularly in resource-limited settings.

The arrangement of this work is as follows: the study's background and context are described in Section 1 of the publication. A literature review is presented in Section 2. The study's methodology is explained in Section 3. Section 4 has described the Fuzzy VIKOR Model and the results of this study's execution, and Section 5 presents a sensitivity analysis. Section 6 of the study's outcomes outlines its distinguishing contributions. The final portion offered concluding comments with limits and future scope.

The literature on supply chain performance enhancement through lean practices and MCDM techniques is extensive. This section reviews the key contributions in three thematic areas: (1) Roles of Telecom Infrastructure in Online Education, (2) performance measurement frameworks and key performance indicators (KPIs) and (3) the application of fuzzy logic and VIKOR in decision-making.

The significance of telecom infrastructure in online education is recognized as essential for enhancing accessibility, elevating quality and decreasing the cost of learning. Research indicates that dependable and extensive telecommunications networks improve access to digital education by ensuring stable internet connectivity, thus narrowing the divide between urban and rural students (Mahenge & Mwangoka, 2014). High-speed internet and mobile networks enable universities to provide interactive learning experiences, including virtual classrooms and multimedia-rich content, which markedly enhance learner engagement (Williams & Eyo, 2011). Moreover, telecommunications infrastructure fosters inclusion by facilitating remote education for marginalized populations, diminishing geographical and economic obstacles (Nazem, Liu, Lee, & Shi, 1996).

In addition to connection, telecommunications infrastructure is essential for cost optimization. Mobile learning platforms and low-bandwidth systems reduce operational expenses while broadening accessibility, rendering education more economical for suppliers and learners (Suresh Kumar et al., 2024). Offline access features, facilitated by telecom-enabled content delivery systems, diminish bandwidth consumption and server strain, guaranteeing uninterrupted learning in low-resource environments (Mahenge & Mwangoka, 2014). Additionally, initiatives such as Brazil's Ceara State Digital Belt exemplify how collaborations between government and telecommunications may deliver universal broadband access, enhancing education and other digital services (Romiszowski, 2013). The literature emphasizes that telecom infrastructure is a supporting technology and a strategic element in attaining egalitarian, scalable and sustainable online education systems.

Telecom infrastructure has a fundamental and revolutionary function in facilitating and enhancing online education, especially in emerging economies such as India, where digital disparities and financial limitations present considerable obstacles. Its many contributions can be thoroughly examined across eight functional categories. After the comprehensive literature review, 24 critical responsibilities of Telecom Infrastructure in Online Education were identified under eight functional categories, as illustrated in Table 1. The initial aspect is Accessibility and Reach, wherein telecommunications networks function as the foundation for last-mile connection, facilitating mobile internet access in remote and underserved areas. Over 90% of the Indian population is served by mobile networks and the growing affordability of smartphones and data plans positions telecom infrastructure as the principal medium for learners without access to broadband or physical educational facilities (Sakhapov & Absalyamova, 2015).

The second category, Communication and Engagement, emphasizes how telecommunications capabilities like SMS, voice calls and IVR (Interactive Voice Response) systems enable prompt communication between educators and learners. These tools facilitate information dissemination and enable two-way interaction, particularly in regions with poor digital literacy or restricted internet access (Bandias & Ram Vemuri, 2005).

Third, in Content Delivery, telecommunications networks facilitate the dissemination of educational material through mobile applications, video streaming services and voice-based instruction (Liang, Hsu, Leu, & Luh, 2005). The capacity to broadcast or download multimedia educational resources across 3G/4G networks – occasionally through zero-rated platforms – improves learning flexibility and accommodates both asynchronous and synchronous instructional approaches Carofiglio, Morabito, Muscariello, Solis, & Varvello, 2013; Sjøvaag, Olsen, & Ferrer-Conill, 2024. The fourth area, Data Analytics and Personalization, utilizes telecommunications usage data (e.g. browsing trends, application interactions, location tracking) to facilitate educational platforms in providing customized learning experiences, adaptive assessments and targeted content recommendations. Data-driven insights enhance comprehension of learner behavior and refine instructional tactics (Drotner, 2005).

Fifth, Learner Support and Assessment is enabled via telecommunications through mobile-based quizzes, SMS feedback forms, helpline services and IVR-based assessments, all of which encourage continuous learning and prompt resolution of student concerns. These tools are essential for sustaining student engagement without physical classrooms (Lamberton, 1996). The sixth category, Cost Efficiency, highlights the economic benefits of telecommunications infrastructure. In contrast to conventional classroom or broadband models, telecom-based delivery systems, particularly those prioritizing mobile, substantially lower infrastructure expenses and facilitate micro-payment alternatives through mobile wallets or prepaid services, enhancing education's affordability and scalability (Basu, Thamrin, Mikawa, Okawa, & Murai, 2007; Wireko, Brenya, & Doshi, 2021).

In the seventh category, Security and Reliability, telecommunications technologies offer robust user authentication via OTP (One-Time Password) systems, secure data transmission and dependable uptime for streaming and communication services. Network redundancy and telecommunications-grade infrastructure enhance service reliability, a crucial element for educational continuity. Marketing, Outreach and Lead Generation constitute a formidable telecommunications function, particularly for academic institutions and EdTech enterprises. Telecom-enabled campaigns, utilizing bulk SMS, missed calls and geotargeted voice messages, have demonstrated significant efficacy in engaging potential learners in regional markets, yielding more qualified leads at a reduced cost relative to conventional CRM-based digital marketing strategies (Cieślik & Kaniewska, 2004).

These eight functional categories collectively encompass the extensive impact of telecom infrastructure on online education. Telecom systems are physical and strategic facilitators of scalable, inclusive and impactful online learning ecosystems by enhancing access and participation, enabling cost-effective delivery, personalized learning and outcome-driven outreach (Bandias & Ram Vemuri, 2005).

Six analytical categories were established to systematically assess the impact of telecommunications infrastructure on online education based on a comprehensive examination of existing research, industry reports and ICT-for-education policy frameworks. Each indicator signifies a unique performance factor corroborated by academic and practitioner-oriented sources.

The first parameter underscores the extent to which telecom-enabled products improve academic achievement. Mobile learning, SMS notifications and IVR interventions have been shown to directly influence course completion rates, dropout rates and learner progress metrics (Castro & Tumibay, 2021; Liu, Sun, & Fu, 2020) contend that learning technologies must provide quantifiable pass rate and retention improvements to warrant widespread use. Consequently, this indicator reflects the enhancement of educational value that the communication infrastructure offers. Financial limitations remain a significant barrier to educational delivery, particularly in developing nations asserted that cost efficiency influences the scalability of e-learning systems. Telecom-enabled techniques must be evaluated based on cost per student, return on investment and content delivery expenses. It emphasizes that affordability is crucial for closing the digital gap in India. This dimension offers an economic perspective to assess the capacity of telecom to generate value at scale.

Digital inclusivity is fundamental to online education, which emphasizes that mobile-first strategies and the growth of rural networks are essential for equal access. Roslan and Halim’s (2021) research highlights network coverage, device penetration and zero-rated access as inclusion metrics. By emphasizing this feature, the framework guarantees that learner involvement in telecommunications is a significant indicator of educational achievement. Metrics like session length, re-engagement and interaction rates underscore telecom-enabled education's motivating and immersive aspects. Liu et al. (2020) showed that mobile interaction elements, such as quizzes and polls, enhance engagement, while it emphasizes the significance of telecom-enabled interactivity in maintaining motivation. Consequently, this measure encapsulates the behavioral aspect of learning success. Telecommunications infrastructure must be dependable and adaptable for online education to operate effectively. Technical studies highlight uptime, streaming efficacy, latency and mistake rates as essential metrics (Wei & Li, 2019). According to Saqr and Alamro (2019), educational institutions cannot meet increasing demand without scalable platforms. This category guarantees that infrastructure is technically sound and prepared for the future.

Ultimately, the function of telecommunications transcends mere access and involvement; it also influences institutional results (Liu et al., 2020; Peng, 2021), emphasizes that educational institutions assess telecommunications tools using conversion measures, such as lead-to-enrollment ratios, certification issuance and job placement rates. Telecommunications serves as both a facilitator of education and a catalyst for institutional sustainability and employable results.

The six factors presented in Table 2, Learning Outcomes, Cost-Effectiveness, Reach & Accessibility, Learner Engagement, Reliability & Scalability and Conversion Efficiency, constitute a comprehensive and verified methodology. They include educational and telecommunications viewpoints, harmonizing pedagogy, economics, technology and institutional efficacy. This multifaceted approach guarantees a thorough comprehension of telecommunications' strategic function in facilitating equitable and sustainable online education, especially in India and other developing market settings.

MCDM methods provide structured approaches for evaluating alternatives under multiple conflicting criteria. Among them, VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje), introduced by, is particularly suited for decision-making where compromise solutions are preferred. The VIKOR method ranks and selects alternatives based on the closeness to the ideal solution, considering both the maximum group utility and the minimum individual regret. It has been effectively used in supplier selection, process optimization and strategy evaluation.

The modified VIKOR was first a tool for advanced MCDM, which can dramatically prove its effectiveness in unclear or vague environments. It helps handle uncertainty and imprecision in real-world decision-making situations. Fuzzy VIKOR is more appropriate than the traditional methods because it uses fuzzy logic to represent approximate values like “high,” “medium,” or “low.” It enables decision-makers to consider conflicting criteria, such as cost vs. quality and find a compromise solution that balances these objectives. The S value represents an alternative to the ideal solution and the R value represents the distance extension from the negative ideal solution. These are measures of the extent to which an intervention follows the criteria and the extent to which it is below the worst case. The Q value is then determined by a weighted formula (using the weighting of the irrelevance of the S and R values) between the S and R values. This value is exploited to rank the alternatives, where smaller Q values correspond to better global performance. Using the fuzzy VIKOR method, the study ranks the interventions according to their overall effectiveness in driving the lean practices, i.e. what strategies are most impactful. The combined approach of FST, sorting and the VIKOR method offers a complete framework to assess and rank interventions for developing lean practices (Chang, 2014). By employing fuzzy ratings to address ambiguity and imprecision in the data, the technique assures that decision-makers will always be in a position to make fully informed judgments based on the best fit and most reasonable representation of the implicit expert opinion (Arif-uz-zaman & Ahsan, 2011). The clustering approach effectively categorizes treatments considering their efficacy and the fuzzy VIKOR method, whose application is straightforward, offers a clear ranking of options according to their overall effectiveness.

To address the ambiguity and imprecision of human judgment in MCDM, researchers have merged fuzzy logic with traditional VIKOR. Fuzzy sets enable decision-makers to communicate judgments using language variables rather than exact numerical values, boosting realism and flexibility (Husain, Maqbool, Haleem, Pathak, & Samson, 2021). Fuzzy VIKOR has been applied in numerous applications, such as sustainable supplier evaluation (Yazdani, Zarate, Kazimieras Zavadskas, & Turskis, 2019), project risk assessment and logistics performance analysis.

However, its applicability in measuring lean supply chain performance remains restricted. This research covers this gap by merging fuzzy logic and VIKOR into a unified framework for measuring the efficacy of lean implementation using a balanced KPI set.

This study adopts a systematic and structured methodology to evaluate the Key Roles of Telecom Infrastructure in Online Education by employing a Fuzzy VIKOR-based MCDM framework. The methodology comprises four distinct levels as illustrated in Figure 1.

Initially, an extensive literature review was conducted to identify the critical roles telecom infrastructure plays in facilitating online education. The review covered academic journals, industry whitepapers, government reports and relevant policy documents to ensure comprehensive coverage. Through this process, a preliminary list of 30 key roles was identified, categorized under nine functional areas. Simultaneously, six performance analysis parameters were prepared based on their relevance to educational effectiveness, accessibility and technical scalability. A structured expert panel discussion was conducted to validate and refine these findings, involving stakeholders from telecom service providers and online education institutions. The panel discussions were held in hybrid mode (online and offline), ensuring broad participation. Based on expert feedback, the initial list was streamlined to 24 key roles, which were grouped under eight functional categories: (1) Accessibility & Reach, (2) Communication & Engagement, (3) Content Delivery, (4) Data Analytics & Personalization, (5) Learner Support & Assessment, (6) Cost Efficiency, (7) Security & Reliability and (8) Marketing, Outreach & Lead Generation. In parallel, the analysis parameters were refined and finalized to six key indicators: (1) Impact on Learning Outcomes, (2) Cost-Effectiveness, (3) Reach & Accessibility, (4) Learner Engagement & Interaction, (5) Reliability & Scalability and (6) Conversion & Outcome Efficiency. The finalized key roles and parameters are shown in Tables 1 and 2.

In the second phase, the fuzzy analytical hierarchy process (fuzzy AHP) was applied to compute the six selected analysis parameters' relative importance (weights). Expert respondents participated in a two-tier interview process, both online and offline, to compare the parameters based on their perceived impact on online education effectiveness. The fuzzy AHP method incorporates linguistic terms, which are then converted into triangular fuzzy numbers, to account for the inherent subjectivity and uncertainty in human judgment. The consistency of pairwise comparisons was checked to ensure logical coherence. Using the Geometric Mean Method, the weights for each parameter were calculated, and the parameters were ranked according to their relative significance in assessing telecom infrastructure roles.

At the third level, the Fuzzy VIKOR method was employed to evaluate and rank the 24 key roles of telecom infrastructure. Expert evaluations were collected based on the performance of each role under the six analysis parameters, again using linguistic terms to capture subjective judgments. These terms were translated into fuzzy numerical values, enabling the construction of a fuzzy decision matrix. The fuzzy VIKOR algorithm was then applied to compute three key indices: the utility measure (S), the regret measure (R) and the VIKOR index (Q). The key roles were ranked based on these indices to determine their relative effectiveness in supporting online education. The VIKOR method allows for a compromise solution, balancing multiple conflicting criteria and identifying strategies closest to the ideal solution.

The final phase involved sensitivity analysis to test the robustness and stability of the proposed rankings. This was achieved by varying the weights assigned to the analysis parameters and observing the resulting changes in the rankings of key roles. This step aimed to assess how sensitive the results are to expert judgment or priority criteria changes. The stability of the rankings under different scenarios reinforces the validity and credibility of the model and enhances confidence in the final decision-making outcomes. This approach ensures the model remains reliable across various contexts and stakeholder perspectives.

The fuzzy AHP was used to ascertain the relative significance of the six chosen KPIs. This approach combines the conventional analytic hierarchy process (AHP) with fuzzy set theory to address expert evaluations' intrinsic ambiguity and subjectivity (Ardjmand & Daneshfar, 2020). Fuzzy AHP is acknowledged as a notable progression in decision-making methods, particularly for allocating criteria weights amongst ambiguity and imprecision (Sivakumar, Radha Krishnappa, & Nallanathel, 2020).

• Phase 1: A hierarchical framework was created, with the primary aim of calculating performance analysis parameters that were prepared based on their relevance to educational effectiveness, accessibility and technical scalability. Six analysis parameters are Impact on Learning Outcomes, Cost-Effectiveness, Reach and Accessibility, Learner Engagement & Interaction, Reliability & Scalability and Conversion & Outcome Efficiency. Pairwise comparisons of the analysis parameters were performed using a fuzzy scale of relative significance grounded on triangular fuzzy numbers (Buckley, 1985). The imprecise comparison matrix Õ is represented as

Each fuzzy number õ = (l, m, u) is defined by a triangular membership function:

• Phase 2: Based on expert assessments, a fuzzy pairwise comparison matrix was developed using Saaty's nine-point scale, adapted to triangular fuzzy numbers. The Geometric Mean Method was employed to compute the fuzzy synthetic extent values for each analysis parameter, allowing for the aggregation of expert judgments, as shown in Table 3.

• Phase 3: To derive crisp priority weights from fuzzy values, the defuzzification using the center of the area (COA) was applied and calculated using the formula:

• Phase 4: The logical consistency of the pairwise comparisons was verified by computing the Consistency Index (CI) and Consistency Ratio (CR) using the following equations:

where $ƛmax$ is the maximum eigenvalue, n is the number of Analysis parameters and RI is the Random Index depending on matrix size.

As per Table 3 and Figure 2, the Fuzzy AHP estimates the relative value of six analysis factors in analysing telecom infrastructure's critical responsibilities in online education. Triangular fuzzy numbers were used to compare each parameter pairwise to capture expert judgments and account for decision-making uncertainty. Table 4 shows Demographic Characteristics of Participants.

The importance and order of the defuzzified weights were determined. Cost-Effectiveness was the most critical indicator with the most significant weight (0.373), placing first among six. This suggests that price and resource optimization are the most essential factors in using telecom infrastructure for online education, especially in resource-constrained countries. Telecom-enabled data systems are crucial for lead generation, admissions and quantifiable educational results, as Conversion & Outcome Efficiency (0.261) ranks second. Learning Engagement & Interaction (0.145) placed third, highlighting the importance of interactive platforms and telecom infrastructure-enabled two-way communication in maintaining student involvement. Impact on Learning Outcomes (0.101) was fourth, indicating its relevance but lesser weight than cost and efficiency aspects. Since the Consistency Ratio (CR) < 0.1, the pairwise comparison matrix is within acceptable limits, indicating logical and reliable judgments by the decision-makers.

The Fuzzy VIKOR method was applied as a MCDM technique to rank alternative supply chain strategies based on the performance of the identified KPIs. The conventional VIKOR method emphasizes compromise ranking and seeks to determine a solution closest to the ideal while accounting for the maximum group utility and the minimum individual regret. Integrating fuzzy logic into the VIKOR model allows the accommodation of imprecision and uncertainty inherent in human judgment, especially when dealing with linguistic terms. The fuzzy VIKOR method is particularly suitable in complex decision-making environments where trade-offs between conflicting criteria must be made under uncertainty (Chang, 2014). This model facilitates the identification of an alternative that provides the most balanced improvement across all KPIs, considering both majority satisfaction (group utility) and individual opposition (regret of the worst criterion).

In traditional decision-making processes, subjective evaluations are typically expected to be stated as accurate numerical values. This offers a substantial problem for decision-makers, especially when assessing solutions based on qualitative criteria. The issue is further amplified in high-risk circumstances, typified by ambiguity and uncertainty, when generating trustworthy decisions becomes incredibly challenging. In response to these restrictions, the emergence of fuzzy set theory has given a viable technique for resolving such imprecision and ambiguity in expert opinions. Traditionally, expert views have been expressed via linguistic factors and instruments such as the Likert scale (Emovon, Norman, & Murphy, 2018). However, the Likert scale is intrinsically restricted in addressing ambiguity since each language phrase is assigned to a set number value, thereby failing to convey the spectrum of vagueness found in human judgment. Fuzzy set theory, by contrast, permits the quantification of language words using fuzzy numbers, enabling a more flexible and realistic depiction of expert evaluations. Triangular Fuzzy Numbers (TFNs) are extensively adopted among the different varieties of fuzzy numbers due to their simplicity and efficacy in capturing imprecision. More recently, improvements in fuzzy logic have led to the creation of three-dimensional spherical fuzzy sets, which provide greater capabilities for handling ambiguity and better capturing the subtlety in expert judgments (Mathew, Chakrabortty, & Ryan, 2020a). While traditional (Type-1) fuzzy sets are useful in simulating ambiguity, they do not resolve uncertainty. Expanded models such as Interval Type-2 Fuzzy Sets (IT2FS) have been developed to circumvent this restriction, providing a more robust representation of uncertainty in decision-making situations (Mathew, Chakrabortty, & Ryan, 2020b).

In light of these advancements, the fuzzy VIKOR technique has evolved as a strong MCDM tool, capable of handling ambiguity and uncertainty while enabling the ranking and selection of options. This research employs the fuzzy VIKOR technique to assess telecom infrastructure's critical responsibilities in online education.The methodological stages required in the fuzzy VIKOR model are detailed as follows:

• Step 1: Let A i where (i = 1,2,3,....n) represent i ^th key roles of telecom infrastructure in online education, assessed against C_j, where j = 1, 2 , . . ., 6 representing the j^th analysis parameters. This MCDM issue is treated in a matrix format, with the performance of each option given using a Triangular Fuzzy Number (TFN), indicated as õ_ij = (l_ij, m_ij, u_ij). The Equation states that the triangle membership function is defined using three absolute values, l, m and u, with vector x.

The research gathered empirical data from 35 respondents from the online education and telecom sectors to ensure a fair view of telecom infrastructure in online education. As indicated in Table 4, participation ranged from senior management (17.1%) to operational and technical personnel (22.9%), providing strategic and functional perspectives. Academic and industrial professionals (25.7%) contributed theoretical and practical expertise to the review. Online education (51.4%) and telecom (48.6%) respondents provided a complete picture of cross-sectoral contacts. With roughly equal representation across categories, 20% had less than 5 years of professional experience, 28.6% had 5–10 years and 25.7% each had 10–15 and more than 15 years. Diversity ensured that emerging and experienced experts influenced judgements, strengthening the analysis.

Further talks with these individuals confirmed the original results, improving the study's methodological rigour and VIKOR analysis's interpretability. This mixed-industry, multi-level and experience-rich dataset is helpful for examining telecom infrastructure's involvement in online education.

• Step 2: Identify and define decision-maker inputs (D1, D2,..., Dk), such as language words and accompanying fuzzy numbers, for each performance criterion and alternative technique. As Table 5 indicates, a TFN fuzzy number represents a collection of linguistic variables. Table 6 describes the decision matrix – the aggregated fuzzy ratings. $õijk$ are appraised about each criterion Cj and may be represented as Equation (6).

• Step 3: Normalization of fuzzy scores ensures they are dimensionless and comparable. For benefit-type criteria:

Non-benefit-type criteria

The decision matrix normalizes and converts data between 0 and 1. The normalized judgment matrix was created to make comparing all features easier and determine the projected value of different options. Equations (7) and (8) provide the formula for normalizing the parameter value. Table 7 shows the normalized fuzzy value.

• Step 4: The normalized fuzzy ratings are multiplied by the corresponding analysis parameters weights (obtained using Fuzzy AHP). The weighted fuzzy matrix is expressed as:

Where $w~j$ is the fuzzy weight for KPI j

• Step 5: Determination of the values $S~i$ and $R~i$ The VIKOR index (Q)

Once the normalized decision matrix is set, each alternative's S (group utility) and R (individual regret) values are computed. The S value shows how close an alternative is to the positive ideal solution, while the R-value shows its distance from the negative ideal solution. These values are obtained from the calculation of the weighted normalized decision matrix.

S represents the total value of each option from the point of view of the group, and R represents the amount of regret that an individual might experience if they select that option. The fuzzy VIKOR method allows both values to be minimized simultaneously and selects the best compromise alternative with the highest utility for the group and the lowest possible regret. Then the values $S~i$ and $R~i$ Can be calculated as follows and is represented in Table 8.

If $R~i=(Ril,Rim,Riu)$ and $s~i=(sil,sim,siu)$

Where

• $f~j*=$ best fuzzy values for each criterion

• $f~j°=worst fuzzy values for each criterion$

The VIKOR index (Q) is a score that combines the S and R values to rank alternatives. It is computed by taking a weighted sum of the distances to the ideal solutions (S) and the distances to the negative ideal solutions (R). In this study, the weight v assigned to group utility is 0.5, indicating that equal importance is given to minimizing group utility (S) and reducing individual regret (R). The value of Q is calculated as follows. If $Q~i=(Qil,Qim,Qiu)$

Where,

The variable v, representing the maximum group utility, is equal to 0.5 in this study.

Table 8 discusses the fuzzy values for S, R calculated for each alternative. These fuzzy values give an all-around view of how each alternative performs relative to the ideal solutions. Table 9 represents the VIKOR Index (Q) and ranking of lean tools shown in Figure 3.

• Step 6: Presentation of a Compromise Solution

Once the values for S, R and Q have been calculated, the required task is to postulate the compromise solution, whereby one must choose the best alternative from the ranking or one or more of the best alternatives. This happens if the two following conditions can be fulfilled:

• Condition 1. “Acceptable advantage: $Q(A(2))−Q(A(1))≥1/(m−1)$ where $A(1)$ is the alternative to the first position and $A(2)$ is the alternative with the second position in the ranking list. Q. m is the number of alternatives”.

• Condition 2. “Acceptable stability in decision making: The alternative $A(1)$ must also be the best ranked by S and/or R”.

If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of:

• Solution 1. “Alternatives $A(1),A(2),….,A(M)$ if Condition 1 is not satisfied, Alternative $A(M)$ is determined by $Q(A(M))−Q(A(1))<1/(m−1)$ for maximum M (the positions of these alternatives are in closeness”).

• Solution 2. “Alternatives $A(1)$ and $A(2)$ if only condition 2 is not satisfied”.

• Solution 3. “The alternative with the minimum Q value will be selected as the best Alternative if both conditions are satisfied”.

Acceptable Advantage: The difference in Q-values between the best and second-best alternatives should be sufficiently significant. This ensures there is a clear winner.

Acceptable Stability: The best alternative ranked must also rank the best in terms of S and/or R.

In this paper, the acceptable advantage condition was not satisfied, which means that the difference is insignificant between the highest-ranking alternatives regarding the Q value. Results of the conditions survey are shown in Table 10.

As a result, a compromise solution was proposed, and the top-ranked alternatives are Employee-Driven Sustainability Initiatives, Behavioral Nudges, Sustainability Innovation Lab, Peer-to-Peer Influence and Eco-Labeling of Products. The options chosen are based on strong performance across all criteria and provide a balance as an effective set of strategies for promoting sustainability.

Sensitivity analysis plays a pivotal role in validating the robustness and stability of MCDM models by examining how variations in input parameters influence output rankings. In the context of the Fuzzy VIKOR methodology, sensitivity analysis is employed to assess how changes in the weight assigned to a particular criterion affect the overall ranking of alternatives. This is particularly important, given that expert judgments and input data in real-world scenarios often contain ambiguity and imprecision (Batwara, Sharma, & Makkar, 2024a)

The fundamental purpose of sensitivity analysis is to discover the effect of specific criterion weights on the final decision result. In MCDM challenges, when decision-makers apply weights based on subjective judgments or historical data, tiny changes in these weights might lead to differing options. Therefore, examining the influence of these differences is vital to guarantee the decision-making model is dependable and resilient in various settings. To undertake the sensitivity analysis in this research, the parameter with the most significant weight, “Cost-Effectiveness”, rated initially at 0.373, was chosen. The “Cost-Effectiveness” weight was systematically changed from 0.1 to 0.5, and the corresponding impacts on the rankings of the 13 lean supply chain methods were noted. As the “Cost-Effectiveness” weight grew, the other five analysis parameter weights were modified to maintain a total normalized weight of 1.

The influence of this adjustment on the Fuzzy VIKOR index values and the ensuing alternate rankings is provided in Table 11. “Affordable Access for the Masses (R16)” consistently retained its position as the top-ranked enabler (Rank 1 in most scenarios “Lead Capture via Telecom (R23)” also remained within the top 2–4 ranks across all values, confirming its robustness as a key enabler. “SIM-Based Authentication (R19)” and “Direct-to-User Campaigns (R22)” showed strong stability, maintaining positions within the top 3–6 ranks in all scenarios.

The analysis validates that the core enablers (R16, R23, R19 and R22) are robust and insensitive to weight variations, making them the most reliable strategic priorities for telecom-enabled online education. Factors with ranking volatility (e.g. R1, R3 and R10) may require context-specific prioritization, where their importance depends on local infrastructure and policy conditions. The persistently low-ranked factors suggest limited practical relevance in current contexts and highlight areas where further innovation or policy support may be required. Additionally, the research indicates that no abrupt rank reversals happened for any of the top-performing alternatives, proving the Fuzzy VIKOR model's applicability in real-world decision situations where input uncertainty is unavoidable (Batwara, Sharma, Makkar, & Giallanza, 2024b). Figure 4 indicates both stability in key enablers and shifts in marginal cases with the parallel plots:

The VIKOR investigation generated a detailed list of telecom-enabled tactics that affect the efficacy of online education. The findings from Table 9 reveal that the paramount element is “Affordable Access for the Masses (R16),” which has the lowest VIKOR index (Q = 0.8271, Rank (1), underscoring affordability as the foremost predictor of inclusive online education. The preeminence of Affordable Access (R16) as the top-ranked factor indicates that cost-sensitive access to telecommunications services is the foremost facilitator for adopting online education in India. Even the most sophisticated digital learning systems cannot attain widespread use without affordable access. Telecommunications data (use patterns, geolocation and application utilization) facilitates identifying appropriate consumers actively engaging with educational or learning platforms. Telecom companies possess knowledge about consumers who regularly use educational websites or applications, enabling institutions to discern genuine interest (Basu et al., 2007; Wireko et al., 2021).

Another highly ranked enabler is “Lead Capture via Telecom (R23, Q = 0.8530, Rank (2).” Numerous educational institutions use CRM (Customer Relationship Management) software to generate leads via digital advertisements, online forms and external databases. These tactics often provide unqualified or less-engaged leads, diminishing conversion rates. CRM lead creation incurs significant expenses, particularly when using platforms such as Google Ads, Facebook or lead marketplaces: dispatch bulk SMS or audio calls directly to specific individuals. Provide USSD-based rapid surveys for interest acquisition. Incorporate mobile number-based opt-in mechanisms (missed calls, flash messages) (Ortiz-Garcés & Villegas-Ch; Wei & Li, 2019). CRM solutions often emphasize email or application-based communication, neglecting regions with limited internet access. Telecom-based outreach (SMS, IVR, missed calls) effectively engages these demographics without needing smartphones or internet connectivity. The third-ranked enabler is “SIM-Based Authentication” (R19, Q = 0.8996, Rank 3). It indicates that both learners and institutions prioritize secure access. Authentication systems address digital trust, fraud protection and fair identity verification, positioning them as a vital enabler in telecommunications (Learn, 1988). “Direct-to-User Campaigns” (R22, Q = 0.9130, Rank 4) illustrate the significance of direct, cost-effective and secure telecommunications attributes in closing the digital divide. Strategies such as “Direct-to-User Campaigns” (R22, Rank 4), “SMS & Voice Notifications” (R4, Rank 8) and “Helplines & Chatbots” (R14, Rank 9) underscore the effective use of telecommunications in disseminating educational information and services to a broad audience, including those with constrained digital literacy. “Reliable Uptime” (R20, Q = 0.9340, Rank 5) underscores the significance of network stability in maintaining continuous online education. It emphasizes that the absence of constant telecommunications services adversely affects online education delivery. This discovery underlines that digital learning quality significantly relies on a strong telecommunications infrastructure.

“IVR-Based Learning” (R5, Rank 6) facilitates course delivery via telephone conversations in local languages, eliminating the need for smartphones. “Shared Infrastructure” (R17, Rank 7) is central, indicating the ongoing significance of conventional telecommunications instruments and cooperative resource usage. “Helplines & Chatbots” (R14, Rank 9) and “SMS & Voice Notifications” (R4, Rank 8) continue to serve as effective support mechanisms for learners, particularly in low-bandwidth or rural environments. Alerts for assignment due dates, examination schedules and live sessions. It is quite economical and does not need internet connectivity. Elements like “Telecom Usage Data” (R10, Rank 10) and “Last-Mile Connectivity” (R1, Rank 11) emphasize the need for network optimization and rural connection. “Zero-Rated Platforms” (R9, Rank 21) received a poor score because of discussions about net neutrality and sustainability concerns. This indicates that politicians and telecommunications providers must reconcile accessibility measures with equitable use restrictions. Telecommunications companies may provide complimentary access (zero-rated) to educational applications and platforms, similar to Reliance Jio's initiative for government e-learning resources. Students may get knowledge without depleting data plans.

“Mobile-First Access” (R2, Rank 16) and “Micro-Payments via Mobile Wallets” (R18, Rank 17) are scored lower, indicating that while mobile penetration is essential, cost and dependability remain more significant than convenience. “Live Streaming of Classes” (R7, Rank 20), “Data-Efficient Content Access” (R8, Rank 19) and “Zero-Rated Platforms” (R9, Rank 21) attained suboptimal scores owing to bandwidth demands, sustainability issues and regulatory intricacies. The least effective tactics include “Regional Outreach” (R24, Rank 22), “Assessment via Mobile” (R15, Rank 23) and “Geo-Fencing & Location Intelligence” (R11, Rank 24), which face scalability, privacy issues or resource demands. The low scores for Live Streaming of Classes (R7, Rank 20) and Geo-Fencing (R11, Rank 24) indicate that, despite their technical sophistication, both techniques encounter obstacles related to cost, bandwidth accessibility and privacy acceptability. Likewise, “Assessment via Mobile” (R15, Rank 23) has a low ranking owing to issues related to legitimacy, usability and reliance on network connectivity. Educational institutions and EdTech platforms must collaborate directly with Jio, Airtel, BSNL and similar entities. Utilize telecommunications data to execute tailored ads in regional languages. It established lead capture using missed calls, SMS codes or USSD menus. It forecasts which consumers are most inclined to convert based on telecommunications use history.

Telecom infrastructure provides a cost-efficient, scalable and precise method for delivering instruction and generating high-quality leads for online school admissions. By optimizing the integration of telecommunications channels (SMS, IVR, mobile data analytics), educational institutions may markedly enhance outreach and lead conversion, particularly in rural and semi-urban India, where conventional digital strategies are inadequate.

This research provided a robust decision-making framework based on the Fuzzy VIKOR approach to assess and prioritize key roles of telecom infrastructure in online education. Incorporating fuzzy logic into the VIKOR approach allows for controlling uncertainty and imprecision inherent in expert judgments, delivering more realistic and relevant decision outputs.

1. Academic implications – The study adds to the scholarly body of knowledge in MCDM by proving the application of the Fuzzy VIKOR approach in the context of lean supply chain strategy selection. It bridges the gap between theory and reality by presenting a structured model that manages fuzziness in expert judgments, which is typically missed in standard decision models. Moreover, this study contributes to the role of telecom in online education by experimentally testing performance indicators and their influence on strategic goals. The ranking outcomes contribute to the literature on digital inclusion, showing that equity and affordability must precede technological sophistication for effective online education adoption.

2. Practical implications – Telecom operators can leverage these insights to design sustainable, learner-centric service models such as micro-payments, direct-to-user campaigns and secure authentication mechanisms to broaden digital education reach. Educational policymakers, the results underscore that ensuring affordable and reliable access (e.g. low-cost data, SIM-based authentication and stable uptime) is essential before introducing advanced digital tools. For educational institutions, the mid-ranked strategies like IVR, helplines and chatbots provide inclusive alternatives for students in low-bandwidth regions, ensuring no learner is excluded due to infrastructural limitations. The sensitivity analysis also equips practitioners with insights into how changes in criteria weights influence strategic outcomes, aiding in more informed and adaptable decision-making.

3. Scientific Contributions- Scientifically, the study contributes to methodological advancements by integrating fuzzy logic with the VIKOR technique to form a hybrid decision-support tool suitable for real-world applications. The study provides a quantitative, validated model for prioritizing telecom-driven online education enablers, filling a critical gap in the digital learning literature. It extends the role of telecom infrastructure beyond connectivity into pedagogical enablement, positioning telecom services as active contributors to educational equity and accessibility. The hybrid Fuzzy AHP–VIKOR application represents a methodological contribution, offering a replicable tool for evaluating ICT-enabled innovations across industries.

4. Limitations and Future Research Directions- While the framework gives valuable insights, several constraints hinder the generalizability of the results. The research was done in northern India with a small sample size and focused on a predefined set of 24 enablers; other emerging factors (e.g. 5G-enabled immersive learning, AI-driven personalization) were not considered. The VIKOR method, while powerful, is sensitive to weighting assumptions from experts, introducing some subjectivity despite fuzzy adjustments. The study also presupposes that decision-makers possess impartial viewpoints and subject competence, which may not always be true. Additionally, being an interpretative study, the results may be vulnerable to alternative interpretations by other researchers. Future studies should expand to cross-country comparative analyses, examining how telecom-enabled education differs across developed, developing and underdeveloped economies. There is scope to integrate longitudinal data to analyze how enabler priorities evolve, especially with rapid technological shifts like 5G, IoT and AI in education. Moreover, different uncertainty modeling strategies, such as probabilistic distributions or interval type-2 fuzzy sets, should be examined to improve decision-making accuracy. The framework also presents an opportunity for longitudinal research to investigate the long-term effect of lean strategy adoption on organizational performance. Further exploration into student-centric outcomes (learning performance, engagement, equity) linked with telecom enablers would bridge the gap between infrastructure and pedagogical effectiveness