Priority Roles of Stakeholders for Overcoming the Barriers to Implementing Education 4.0: An Integrated Fermatean Fuzzy Entropy-Based CRITIC-CODAS-SORT Approach

This work deﬁnes various stakeholder roles (or strategies) to overcome the barriers to implementing Education 4.0 (EDUC4), which were recently identiﬁed in the domain literature. The stakeholder roles are evaluated against these barriers, and such evaluation is structured as a multicriteria sorting problem. To this end, an integrated entropy-based CRITIC-CODAS-SORT under a Fermatean fuzzy (FF) environment addresses epistemic uncertainties inherent in decision-making. The FF CRITIC assigns the priority weights of the barriers, while the FF CODAS-SORTdetermines the high-priority stakeholder roles. A case of an HEI evaluating 57 possible roles of 5 stakeholders is demonstrated here. Findings suggest the lack of collaboration, apprehensive stakeholders, cybersecurity threats, health issues, and cost as crucial barriers to the HEI. The sorting process yields 13 high-priority roles, encompassing those within the inﬂuence of the government (i.e., cybersecurity awareness, allocation of necessary funds, designing more aligned curricula, and streamlining the basic education agenda), university management (i.e., investing in eﬃcient technologies and forging extensive stakeholder collaboration), human resource function (i.e., implementing periodic skills training for educators), and educators (i.e., engaging in continuous learning about cybersecurity threats, integrating awareness of applicable laws against cyberbullying, devising alternative cost-eﬃcient teaching strategies, taking part in initiatives to improve curricula, eﬃcient preparation of learning materials, and participating in skills development initiatives). Various managerial insights are oﬀered as inputs to the design of initiatives in EDUC4 implementation.


Introduction
In recent years, Education 4.0 (EDUC4) has been recognized as a framework for learning institutions so that teaching and learning will be aligned with the fourth industrial revolution (4IR). EDUC4 characterizes a learning process highly associated with technologies such as virtual learning environments [1], adaptive internet of things (IoT) [2], and artificial intelligence (AI) [3]. ese technologies have a curriculum design that reflects technology-based environments [4]. Despite these advances in the teaching-learning process linked to EDUC4, developing economies encounter barriers in its implementation due to resource scarcity, educational politics, and cultural aspects. For instance, the response of Malaysia in EDUC4 faces challenges ranging from limited and inefficient educational resources, outdated teaching styles, and inadequate infrastructure, to a lack of close linkages among educational institutions [5]. In Pakistan, they found no framework that provides the base for EDUC4 with the lack of resources, improper implementation of relevant policies, and inexperienced human resources [6]. A recent review by Costan et al. [7], with an empirical work of Gonzales et al. [8], comprehensively identified these EDUC4 implementation barriers, with a particular focus on developing economies. Current literature (e.g., [3,9]) highlighted some essential roles of stakeholders in overcoming the barriers of implementing EDUC4 and putting such an initiative into action. Although Costan et al. [7] established the barriers through a systematic literature review, there is no existing literature about identifying specific functions of the stakeholders that can better address the barriers to EDUC4 implementation, especially in a developing economy. Mourtzis [10] reported the relevance of the teaching factory concept for successful EDUC4 implementation, but the degree of participation of the stakeholders so that a university could dynamically execute the teaching factory direction is not clear. is implies that stakeholders' roles in taking the EDUC4 initiative are not straightforward. For instance, we expect to improve government investments in social and human capital [11] and prepare for the costly challenges of rapid technological advancements and developing ICT competencies.
us, overcoming the barriers to EDUC4 implementation needs a thorough understanding of stakeholder roles so that educational managers, human resources, educators, ICT function, and other relevant stakeholders can function systematically in any policy direction toward EDUC4.
In this work, evaluating stakeholder roles in overcoming different barriers to implementing EDUC4 is structured as multiple-attribute decision-making (MADM) problem, where barriers are treated as "evaluation criteria" and stakeholder roles as "evaluation alternatives." In addressing this problem, we proposed the integration of the CRiteria Importance through Intercriteria Correlation (CRITIC) and multiple criteria sorting (MCS) method based on the COmbinative Distance-based ASsessment (CODAS) approach (i.e., CODAS-SORT) under Fermatean fuzzy set (FFS) environment to account for epistemic uncertainties in expert decision-making. e Fermatean fuzzy (FF) CRITIC assigns priority weights of implementation barriers, while the FF CODAS-SORT sorts the stakeholder roles by identifying those high roles for strategic implementation of EDUC4. Unlike other priority weight allocation methods (e.g., analytic hierarchy process, best-worst method, and full consistency method), the CRITIC developed by Diakoulaki et al. [12] provides an efficient technique for generating priority weights of criteria or attributes from a decision matrix. e mental workload required from decisionmakers in eliciting judgments is significantly minimized, particularly in a huge number of attributes (e.g., 50 attributes). Recent applications of the CRITIC method were reported in the MADM literature (e.g., [13][14][15]). On the other hand, the CODAS method, proposed by Ghorabaee et al. [16], offers an efficient yet powerful MADM platform based on Euclidean distance, similarly conceptualized with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Such applications of the CODAS and its extensions have been increasing in the literature (e.g., [17][18][19]). e CODAS-SORT, with a variant offered by Ouhibi and Frikha [20], is part of the family of MCS methods that assigns a set of elements (e.g., alternatives) to predefined classes under an evaluation based on multiple criteria. A brief discussion of the background of MCS is found elsewhere (e.g., [21]), and the performance of the CODAS-SORT is found to be comparable with TOPSIS-SORT and VIKORSORT [21,22], but with a more efficient computational framework.
Due to the presence of vagueness and uncertainty inherent in both CRITIC and CODAS-SORT, the use of the FFS addresses these conditions by overcoming the limitations of the classical fuzzy set [23] and the intuitionistic fuzzy set [24] or the Pythagorean fuzzy set [25]. is particular argument on epistemic uncertainties has been repeatedly mentioned in several other works in the field of management [26][27][28]. Proposed by Senapati and Yager [29], the FFS is deemed more capable of handling higher uncertainties than the previously developed fuzzy environments. Although the FF CRITIC has been recently offered in the literature [30,31], the integration of FFS within CODAS-SORT is not yet explored, so is the application of an integrated FF CRITIC-CODAS-SORT in an MADM problem. is forms the methodological contribution of this work. A case study in a publicly funded HEI in the central Philippines demonstrates the application of the proposed approach. Ultimately, the main contributions of this work advance both the literature on EDUC4 and MCS by developing an integrated approach based on FF CRITIC-CODAS-SORT in systematically identifying high-priority stakeholder roles in overcoming the barriers to EDUC4 implementation. Determining these important roles would inform the design of initiatives and policy directions of different stakeholders in advancing the implementation of EDUC4 in an HEI. e remainder of this paper is arranged as follows. Section 2 reviews the relevant literature. Section 3 presents some background of FFS, the CRITIC, and CODAS methods. Section 4 details the methodology by illustrating the case study environment and demonstrates the application of the proposed FF CRITIC-CODAS-SORT in identifying the highpriority stakeholder roles. e findings and some key policy insights are discussed in Section 5. It ends with concluding remarks and a discussion of future works in Section 6.

Literature Review
Previous works have investigated the barriers to EDUC4 implementation in various aspects: human resources [2,3], change management [32], technological infrastructure [33,34], and financial [35], among others. A systematic literature review by Costan et al. [7] reported a comprehensive identification of the barriers to EDUC4 in developing economies. In their work, 12 barriers were identified. ese barriers include cybersecurity threats, costly, skill gap of the human capital, apprehensive stakeholders, lack of training resources, lack of collaboration, knowledge gap for the customization of curriculum design, insufficient available technologies, health issues, time constraint for material preparation, the complexity of learning platforms, and insufficient foundation in basic foundation. e initiatives in addressing these barriers are complex, and the policy directions are ideally dependent on economic characteristics and the willpower of the stakeholders. Notably, the implementation strategies are contextually unique, and there is a need to capture the evidence of changes among the key players, such as the policy-makers, educators (enablers), and learners (receivers) [4]. For example, a study on the design framework for Indonesian higher education using blockchain technology (i.e., an EDUC4 component) concentrates on investing in human resources and social capital [11].
As part of the clusters of barriers identified by Costan et al. [7], managing human resources requires the need for a sustainable program that enhances labor market demands, such as upskilling and reskilling of university graduates aligned with the requirements of the industries [36] to increase productivity [6] and harmonize human and artificial intellectual capital [3]. e policies and practices necessary for upgrading human resources are imperative in EDUC4 implementation. On the other hand, as a technology-based environment, EDUC4 requires ICTs to be integrated into the teaching-learning process. In Malaysian Schools, Ghavifekr and Wong [37] suggest that the utilization of ICTs and the digital revolution have been the focal points in this direction. ey demonstrated that the ICT leadership of school principals impacts teachers' effective ICT utilization. Finally, as front liners in the implementation process, the role of educators in exercising the strategic initiatives of the HEI managers is equivalent to the quality of the target competencies. Hamilton [34] postulated teachers' human side efforts while working with AI and other technologies in a university experience. Customized adaptive learning, redefined assessment, and intelligent and smart approaches are some initiatives for enhanced delivery of learning outcomes under an EDUC4 environment.
Previous studies revealed that stakeholders, that is, government, university management, human resource function, ICT function, and educators, play crucial roles in implementing EDUC4 [3,9,34]. e macro-level role of the government goes beyond policy-making and funding sources. For instance, in the Philippines, the government and its faculties are committed to the following functions: (1) provide training to educators for lesson delivery, curriculum design, and instructional materials development, (2) align and device initiatives that will complement basic education and EDUC4, (3) craft protocols to safeguard from cybersecurity attacks and to promote healthy use of technologies, (4) strengthen collaboration efforts from internationally recognized higher education institutions (HEIs) and intragovernment agencies, (5) benchmark technologies used by successful implementers of EDUC4, and (6) ensure and evaluate that EDUC4 responds to the sustainable development goals. Moreover, the government's massive role in EDUC4 translates to the seamless coordination between delivering agencies and the HEIs. As a decision-making body, the role of HEI managers is to carry out strategic initiatives to achieve target goals, including pedagogical and evaluation assessments, relevant approaches to promote cybersecurity awareness, applicable measures in learning material preparation, and essential and cost-efficient technologies for content delivery.
Different findings emerged in the literature on EDUC4 implementation. For example, Ramírez-Montoya et al. [38] identified that decision-makers and the social and academic communities play important roles in developing reasoning for complexity. Critical thinking competency has been given importance in the EDUC4 framework in their work. us, HEIs must understand that training in complex reasoning is necessary for the academe. Gonzales et al. [8] identified that the financial aspect and lack of training resources are the most prominent barriers among developing economies. HEIs shall take the primary responsibility for overcoming these barriers. As supported by González-Pérez and Ramírez-Montoya [39], the need to incorporate educational practices into the core components of EDUC4 becomes imperative. ey added that schools and teachers do not possess the twenty-first-century skill frameworks with the EDUC4 components to develop future skills. e school leadership towards ICT utilization impacts teachers' active ICT utilization, leading to an increase in students' academic performance [37]. e IT integration in schools towards the EDUC4 system has been a great challenge among administrators. López et al. [40] highlighted that leadership in EDUC4 can lead to students' success in attaining the skills and competencies to become IT leaders in modern industries. Due to the university's decentralized design, instructors might use whatever other technology they consider appropriate for their classes at the risk of losing official backing [41]. e ongoing training for using digital educational resources and their integration into traditional practices is important to ease the transition process, with the COVID-19 crisis emphasizing such importance.
Likewise, the need to fully align the practices of various academic disciplines into the EDUC4 framework is discussed in the literature. For example, Bilotta et al. [42] revealed that methods and technologies introduced by big data, automation, virtual and augmented reality, robotics, and ICT will fit with EDUC4, with a case in the tourism industry. Still, the students are not yet trained on techniques, issues, and methods related to the emerging framework. Goldin et al. [43] proposed an architecture to help users recognize how to digitalize education and create a better plan on how EDUC4 can be implemented into the IT landscape of the universities. Another stream emphasizes that professors must possess competencies for innovation, complex problem-solving, entrepreneurship, collaboration, international perspective, leadership, and connection with the needs of society [33]. Emerging literature also focuses on the alignment to engineering education, emphasizing that the education sector mainly benefits from the recent technological progress [9]. ey proposed the four core components of EDUC4 in higher education: (1) competencies, (2) learning methods, (3) ICTs, and (4) infrastructure. e 4IR requires that the education system do everything in time Complexity 3 to support the transformation of the curriculum with the requirements of EDUC4 [44]. us, it is evident in the literature that the roles of stakeholders are always linked to the EDUC4 transition, either implicitly or explicitly. However, despite the need to systematically understand these roles, the current literature offers limited insights.

Fermatean Fuzzy Set.
e fuzzy set theory has been wellregarded for dealing with imprecise information and uncertainties. It was developed primarily by Zadeh [23] as an application for the numerous valued logic to illustrate the behavior of complex electrical systems. An extension of the fuzzy set theory was introduced by Atanassov [24], which is the intuitionistic fuzzy set (IFS). It is characterized by a membership function, a non-membership function, and a hesitancy degree that expresses support, opposition, and neutrality in eliciting information [24], extending the concept of membership functions of Zadeh's fuzzy set theory. It is defined as follows: Definition 1 (see [24]). Let Δ be a non-empty universe of discourse. e IFS F has the general form and ] F (x) refer to the degree of membership and degree of non-membership of the element x ∈ Δ in the set F, respectively. However, in practical application, decision-makers may elicit their judgment fulfilling a set condition either to an assisting or opposing degree greater than 1. us, Yager [25] introduced the notion of Pythagorean fuzzy sets (PFS) to address this possible condition, whose illustration is given as follows: Definition 2 (see [25]). Let Δ be a non-empty universe of discourse, and the PFS P can be presented as follows: where μ P (x): Δ ⟶ [0, 1] and ] P (x): Δ ⟶ [0, 1] such that 0 ≤ ( μ P (x)) 2 + (] P (x)) 2 ≤ 1 for all x ∈ Δ. Furthermore, μ P and ] P (x) refer to the degree of membership and degree of non-membership of the element x ∈ Δ in the set P, respectively. For any P and x ∈ Δ, the degree of indeterminacy, π P (x), can be calculated by However, the PFS could not handle certain conditions. For instance, μ P � 0.9 and ] P � 0.6 suggest that 0.9 2 + 0.6 2 ≤ 1. us, Senapati and Yager [29] proposed the notion of the FFS to provide a tool for handling uncertain information more efficiently and is more flexible in capturing uncertain information than IFS and PFS. e features and operators of FFS are defined as follows: Definition 3 (see [29]). Let Δ be a non-empty universe of discourse. e Fermatean fuzzy set T in Δ can be presented as follows: where and ] T (x) refer to the degree of membership and degree of non-membership of the element x in the set T, respectively. Meanwhile, the degree of indeterminacy, π T (x), is identified through (5) Figure 1 shows the difference among the spaces related to intuitionistic membership grades (IMG), Pythagorean membership grades (PMG), and Fermatean membership grades (FMG). In general, these fuzzy sets are part of a class of q-rung orthopair fuzzy sets in which the sum of the q th power of the membership function and the q th power of the non-membership function is bounded by 1 [45]. For instance, q � 1 implies IFS; q � 2 implies PFS.
Definition 4 (see [29]). Suppose that T � (μ T , ] T ), T 1 � (μ T 1 , ] T 1 ), and T 2 � (μ T 2 , ] T 2 ) are three distinct FFS and α > 0, then the following are the operators for the FFS: 3.2. e CRITIC Method. Diakoulaki et al. [12] initially proposed the CRITIC method, which determines the priority weights of elements of a given set through an aggregation process. Accordingly, the underlying notion of the CRITIC method is the significant information that can be drawn from the criteria set that contains the contrast and conflict concentration between criteria [12,48,49]. e contrast intensity and degree of variability among scores within the criterion are captured through computing the standard deviation. Additionally, the CRITIC method obtains the pairwise linear correlation coefficients among criteria in evaluating their conflicting relationships. us, CRITIC collectively analyses sufficient information contained in the set of evaluation criteria and, in general, the set of homogeneous decision elements.
Definition 9 (see [12]). Let U be a finite set of m alternatives. en, given a system of n evaluation criteria c j (j � 1, . . . , n), the MADM problem in its general form is presented as follows: In this case, for every criterion c j , a membership function x j is defined that maps the values of c j to the interval [0, 1]. is transformation is based on the concept of the ideal point. us, a value close to the ideal c * j is the best performance in criterion j and close to the anti-ideal value c j * is the worst performance in criterion j. e steps in determining the criteria weights using the CRITIC method are as follows. Note that, in general, the criteria set can be a set of any homogeneous decision elements.
Step 1: Determine the set of n criteria and m alternatives constructed as a hierarchical MADM problem.
Step 2: Evaluate the performance score a ij of the i th (i � 1, . . . , m) alternative with respect to the j th (j � 1, . . . , n) criterion.
Step 3: Compute the normalized matrix X � (x ij ) m×n where the normalized score x ij describes a linear normalization of a ij scores and represents where a * j � max i a ij and a j * � min i a ij for j � 1, . . . , n.
Step 4: Generate a vector x j denoting the normalized scores of all m alternatives. Vector x j is calculated using the following equation: Step 5: Compute the standard deviation of each x j by the following formula:

Complexity 5
where x j � m i�1 x ij /m. Aside from standard deviation, Diakoulaki et al. [12] suggest that the use of entropy or variance is also possible.
Step 6: Construct a symmetric matrix R � (r jk ) n×n where r jk denotes the linear correlation coefficient of two vectors x j and x k , j, k ∈ 1, . . . , n { }, using the following formula: where r jk ∈ [−1, 1]. Obviously, when j � k, then r jk � 1.
Step 7: Compute the amount of information z j as follows: where the higher value of z j implies that the criterion j contains more information.
Step 8: Determine the criteria weights according to the following formula:

e CODAS Method.
e CODAS method was initially proposed by Ghorabaee et al. [16], wherein the desirability of the alternatives is determined based on l 1 -norm and l 2 -norm indifference spaces for criteria. In this method, a combinative form of the Euclidean distance and the secondary measure, Taxicab distance, is used to calculate the assessment score of alternatives wherein the alternative has a greater distance from the negative ideal solution is more desirable. e steps of the CODAS method for MADM problems are presented as follows: Step 1. Construct the decision matrix A that is represented as follows: where a ij ≥ 0 denotes the performance value of i th (i ∈ 1, 2, . . . , m { }) alternative with respect to the j th (j ∈ 1, 2, . . . , n { }) criterion (or attribute).
Step 2. Determine normalized decision matrix N � (n ij ) m×n according to the type of each criterion using the linear normalization of performance values as follows: where P and C represent the sets of benefit and cost criteria (or attributes), respectively, and n ij denotes the normalized performance values.
Step 3. Calculate the weighted normalized decision matrix B � (b ij ) m×n as follows: wherein n j�1 w j � 1, w j denotes the weight of the j th criterion, and 0 < w j < 1. w j can be determined through any priority weight generation method (e.g., CRITIC).
Step 4. Determine the negative ideal solution as follows: Step 5. Calculate the Euclidean d i and Taxicab t i distances of alternatives from the negative ideal solution using the following equation: Step 6. Construct the relative assessment matrix H � (h ik ) m×m presented as follows: where k ∈ 1, 2, . . . , m { } and β is a threshold function that can be set by the decision-maker and defined as follows: If the difference between the Euclidean distances of the two alternatives is less than ρ, then these two alternatives are also compared by the Taxicab distance.
Step 7. Calculate the assessment score (S i ) of each alternative as follows: wherein the alternative with the highest S i value is the most desirable. Given the simplicity of the CODAS for the decision-makers and its success, a sorting method was developed by Ouhibi and Frikha [20] called CODAS-SORT. In an MCS problem, the decision-maker aims to assign alternatives to predefined classes. For brevity, the steps of the CODAS-SORT are not repeated here. Despite the introduction of the CODAS-SORT, some technical issues in the sorting process proposed by Ouhibi and Frikha [20] are evident, which prompted an introduction of a modified CODAS-SORT variant, along with the integration of FFS.

Case Study Background.
To keep up with the consequential dynamics that continue to reshape life, economies, industries, and jobs in developing economies, HEIs should embrace the emerging trends of EDUC4, including personalized learning, remote learning opportunities, an abundance of educational tools, project-based learning, and innovation-based education. In this context, the curriculum and learning outcomes require twenty-first-century skills to address the urgency of essential modernization. Current reports predict that AI will transform the hiring behavior of tech-driven companies. Calibrating to the industry requirements propels the HEIs to remodel their curriculum to integrate life skills into the programs through immersion with real-world stakeholders such as the industry, society, and entrepreneurial networks. Government investments with industry and local society across all aspects of the education value chain, from curricula and faculty to infrastructure, research, study experience, and placements, should expand partnerships. e collaborative models with global experts from academia and industry should also advance in-site research opportunities for small and medium enterprises with limited research groundwork. e faculty may be able to develop a group of champion faculty members coming from different departments who are leading the way in developing digital skills or new innovative teaching techniques utilizing various technologies.
Cebu Technological University (CTU) Danao Campus is a component campus of the CTU, a state university in the central Philippines. Following existing guidelines in Philippine institutions, the operating expenditures among state universities and colleges for personnel services, maintenance, and other operating expenses and the capital outlays are coming from government subsidies allocated through the General Appropriations Act (GAA)-the annual national expenditure budget of the government. Aside from the GAA funds, incomes are also generated from various fees and grants provided by international and local institutions. With the recent rise of the university in various rankings and its expanded role in the national development agenda, CTU is pushing for innovation efforts in its different functions, including instruction and research. Among these efforts is directed towards attaining an environment fostering EDUC4. Since CTU Danao Campus is positioning itself as a globally competitive campus of the university and alignment to EDUC4 is inevitable, efforts are becoming grounded for its realization. Although efforts and activities are evident, an integrative framework, particularly on the design of these initiatives, is missing. e government resources remained significantly deficient to support the massive task to consolidate the efforts to address barriers related to financial resources and to recalibrate CTU to stay relevant in the age of EDUC4, resulting in struggling levels of university-industry collaboration, insufficient industry-relevant research consortiums, and underdeveloped research infrastructure and cutting-edge laboratories and equipment. e initiatives of CTU 4.0 transformation, coined by the university through EDUC4, are underway; however, government funding priorities should be enforced not only for the operating expenditures but also for the innovation disbursements targeting the significant deficiencies in attaining the inevitable EDUC4 transformation to become a globally competitive educational institution. Although the Philippine government's spending on public higher education exhibited an upward trend, the corresponding increase in government appropriation to state universities means that these universities shall prioritize expenses to expedite solutions for the implementation barriers to enhance research funding, talent, infrastructure, and links with the industry. However, there are inadequate policies, mechanisms, and understanding of how these barriers will be directed. One possible direction is that the constrained allocation of public funding should move toward a performance-based approach for campus research and capital expenditures to concentrate on attaining EDUC4.
In this regard, following a series of strong evidence in the literature, stakeholders play a substantial role in guiding the university for the design, planning, and implementation of any initiative, which includes the direction leaning toward EDUC4. In the current setting, the following stakeholders are relevant for CTU Danao: (1) the Philippine government (i.e., represented by the trifocal agencies Commission on Higher Education (CHED), Department of Education (DepEd), and Technical Education and Skills Development Authority (TESDA)), (2) university management (i.e., from the top management down to academic departments), (3) human resource, (4) ICT function, and (5) educators. Identifying the crucial roles of these stakeholders in systematically overcoming the barriers of EDUC4 implementation is an essential agenda for CTU Danao in its efforts for EDUC4. is agenda would help establish institutionallevel policies to describe the impacts, show findings, and provide recommendations for a conceptual-analytical framework for implementing EDUC4. Furthermore, although idiosyncrasies exist, the insights would yield comparative results with other developing economies' strategic priorities and policy actions addressing implementation barriers. Figure 2 shows the methodological framework of the Fermatean fuzzy CRITIC-CODAS-SORT approach in establishing the degree to which the stakeholder roles overcome the barriers of EDUC4 implementation.

Complexity
Note that due to idiosyncrasies, the implementation of the proposed framework is intended for a single case (e.g., an HEI). e proposed methodological framework consists of two main phases: (1) obtaining the priority weights of the barriers to EDUC4 implementation through FF CRITIC and (2) sorting the stakeholder roles in addressing these barriers via FF CODAS-SORT. In this framework, the weights generated from phase (1) are integrated into phase (2). e application of the proposed approach is discussed as follows: Step 1. Identify the roles of stakeholders. is study identified the roles of stakeholders in overcoming the barriers to EDUC4 implementation of a case university (i.e., CTU) through a focus group discussion of domain expert decision-makers. ey were chosen in such a way that satisfies the following qualifications: (1) must be affiliated with the HEI in the case environment, (2) must have a PhD degree, (3) must have at least five years of experience in a supervisory or administrative function, and (4) must have at least five years of experience working with the HEI in the case environment. As shown in Table 1, five stakeholders, that is, government, university management, human resource function, ICT function, and educators, were identified along with their corresponding roles in overcoming the barriers identified by Costan et al. [7] (see Table 2). In the case study, the government comprises frontline institutions consisting of the CHED, DepEd, and TESDA.
ey are the trifocal institutions associated with the educational system in the Philippines. e university management consists of those in the organizational hierarchy ranging from the chairs of the academic departments, deans of colleges, campus directors, vice presidents, and president, to the board of regents. e human resource function oversees the functional areas of human resource management, including staffing, development, compensation, safety and health, human resource information system, and employee and labor relations. On the other hand, the ICT function manages communication, data management, cybersecurity, and technology development. Lastly, the educators represent the teaching staff of the university.
Step 2. Obtain the FF initial decision matrices. Initial ) represents the degree of relevance of stakeholder role i in overcoming a barrier to EDUC4 implementation j elicited by the k th decisionmaker in linguistic terms, were constructed. ese matrices were transformed into FF decision matrices using the linguistic scale shown in Table 3.
Phase 1. Implementation of the FF CRITIC. e processes in steps 3 to 5 discuss the integration of FF CRITIC in assigning priority weights to barriers to EDUC4 implementation.
Step 3. Construct the aggregate FF decision matrix. e aggregate FF decision matrix A � (a ij ) m×n is Identify the roles of stakeholders in overcoming the barriers of EDUC4

Start
Obtain the FF initial decision matrices.
Construct the aggregate FF decision matrix.
Obtain the de-fuzzified aggregate decision matrix.
Generate the priority weights of barriers to EDUC4 implementation.
Assign the roles of various stakeholders to their corresponding classes.
Determine the Euclidean and Taxicab distances.
Obtain the negative-ideal solution.
Construct the augmented matrix.
Identify an ordered set of predetermined classes based on priority levels. End Construct the relative assessment matrix.
Obtain the symmetric matrix.

U17
Engaging in initiatives in promoting cybersecurity awareness among university members (i.e., educators, learners, and staff)

U18
Designing measures that are security-cognizant (e.g., centralized IT governance, uniform control, segregation of networks, enhanced strategic alignment, and accountability), including stringent access regulators to shield sensitive data and information U19 Investing in efficient technologies (e.g., virtual classrooms, enablement or process audit, analytic tools for strategic planning, and the hybrid or fully automated process of project management), which are known to reduce overall costs and improve the experience of the university stakeholders U20 Constant training and capability upgrading of educators in terms of technical competencies and behavioral stamina for supporting adaptability, reliability, productivity, and total well-being as they align with the demands of EDUC4

U21
Fostering transformational support and environmental and institutional framework for university educators, learners, and staff for adapting to the EDUC4 atmosphere

U22
Engaging stakeholders in dialogues that emphasize the alignment of EDUC4 with global inclusive agenda (e.g., UN-SDGs)

U23
Exploring the translation of the EDUC4 framework into pedagogy, assessment, and the design of an instructional system U24 Forging extensive collaboration with various stakeholders (e.g., policy-makers, academic experts, university networks, educators, education leaders, learners, and industry partners) to provide space and training resources for implementing EDUC4

U25
Benchmarking of established and favorable practices for EDUC4 implementation

U26
Establishing measures that would allow more time for the educators in preparing learning materials, conducting research and development projects, and attending to continuous learning opportunities inclined to EDUC4 Complexity 9 Establishing holistic initiatives for linkage and collaboration with foreign universities, industry, non-government organizations, government offices, and international organizations, among others, in the delivery of intended 10 Complexity constructed, where a ij is obtained using equation (9) and w i is the corresponding weight of k th decisionmaker. In this study, the length of service holding a supervisory or managerial position and level of administrative function were used to assign weights to decision-makers. Following the agreement of the decision-makers, the following are used to generate their importance weights to the decision-making problem. To give more credit to their current administrative functions, the scores of 5, 4, 3, and 2 are assigned to Campus Director, Assistant Campus Director, Dean, and Program Chair, respectively. For instance, the importance weight of DM3 is computed as: 0.2022 � 14/87 * 4/3.1839, where 14 is the number of years holding a supervisory or managerial position, 87 is the sum of column (2) of Table 4, and 3.1839 is the sum of all products of normalized column (2) and the scores associated with their current administrative functions of all decision-makers. Analogous to equation (9), A is shown in Table 5, where   where w k is the importance weight of k th decisionmaker.
Step 4. Obtain the defuzzified aggregate decision matrix A. e defuzzified aggregate decision matrix A � (a ij ) m×n was obtained using equation (10) to transform the aggregate evaluation scores in FFS to their corresponding crisp (non-FFS) values. e resulting matrix is shown in Table 6. Instead of equation (15), the entropy e j method was used in this work as presented in the following equation: Step 5. Obtain the symmetric matrix R. e symmetric matrix R was constructed using equation (16) and is shown in Table 7.
Step 6. Generate the priority weights w j , j � 1, . . . , m, of barriers to EDUC4 implementation. e information value z j is calculated using equation (17). Furthermore, the two values, e j and z j , are used to obtain the priority weights w j using equation (18). e w j values are presented in Table 8.

Phase 2. Implementation of the FF CODAS-SORT
Here, steps 6 to 10 discuss the application of FF CO-DAS-SORT in sorting the roles of various stakeholders in overcoming the different barriers to EDUC4 implementation.
Step 6. Identify an ordered set of predetermined classes based on priority levels. In general, L (e � 1, . . . , L) classes can be predefined for the MCS process. ese classes generate L − 1 limit profiles. Each e class contains lower and upper boundaries, denoted by l a e and l b e , where l b e � l a e+1 . In this work, L � 3 classes (i.e., low relevance, moderate relevance, and high relevance) and two limit profiles are introduced.
Step 7. Construct the augmented matrix A. e aggregate FF decision matrix in step 3 with the L − 1 limit profiles identified in step 6 is used to construct the augmented matrix A � (a ij ) m×n . e resulting matrix is presented in Table 9.
Step 8. Obtain the negative ideal solution b * . A was used to obtain the negative ideal solution b * � (b j * ) 1×n using equation (23). Considering that the elements in A are FFS, then Definition 7 and eorem 1 discussed in Section 3.1 were used to obtain b * . e resulting vector is illustrated in Table 10.
Step 9. Determine the Euclidean and Taxicab distances.
e Euclidean distance D i (a ij , b j * ) between each stakeholder role i (including the limit profiles) and the ideal negative solution b j * obtained in step 8 is calculated using the following equation: where w j represents the priority weights of barriers to EDUC4 implementation obtained from FF CRITIC in step 5 in Section 3.2 and d(a ij , b j * ) is calculated using equation (11).
On the other hand, the Taxicab distance t i (a ij , b j * ) between each stakeholder role i (including the limit profiles) and the ideal negative solution b j * obtained in step 8 in Section 3.2. is calculated analogously using equation (25). Considering that both elements are FFS, equation (7) was used to obtain their difference. en, equation (10) was used to transform the obtained Taxicab distance t i (a ij , b j * ) to their corresponding crisp value t i (a ij , b j * ). Both the Euclidean and Taxicab distances are shown in Table 11.
Step 10. Construct the relative assessment matrix. Following step 6 in Section 3.2, the relative assessment matrix H � (h iκ ) m×L−1 is calculated, where h iκ is shown in equation (32), and the resulting matrix is featured in Table 12. e threshold parameter is set to be ρ � 0.02.
Step 11. Assign the roles of various stakeholders to the predefined classes. Suppose that h iκ (L2) is the highest limiting profile, then the stakeholder role i can be classified as follows:    class L low if h ik (L2) < 0 and h ik (L1) < 0.
e final classification of the roles of various stakeholders to overcome barriers to EDUC4 implementation is illustrated in Figure 3.

Results and Discussion
In promoting a workable EDUC4 implementation roadmap, this work offers the application of the proposed FF entropybased CRITIC-CODAS-SORT in evaluating the stakeholder roles for overcoming the barriers to implementing EDUC4. e applicability of the proposed framework is positioned to analyze the conditions describing an HEI. In the proposed approach, the FF CRITIC determines the priority barriers, while FF CODAS-SORT identifies the high-priority stakeholder roles that could guide the case HEI in formulating policy directions appropriate for its implementation of EDUC4. Identifying the relevant and priority barriers is essential for an HEI at different managerial levels to accomplish activities attuned to addressing these barriers. A set of expert decision-makers at the university level elicited judgments on the relevance of various stakeholder roles in overcoming the barriers to implementing EDUC4 in developing economies recently identified in the literature. Consequently, the insights generated strategic views to design appropriate approaches for the implementation agenda. Results show that the top five most relevant barriers associated with the case HEI in developing initiatives for EDUC4 implementation are the lack of collaboration (B6; i.e., external fund sourcing and industry linkages), apprehensive stakeholders (B4; i.e., low motivation, fear of the unknown and limited technical know-how), cybersecurity threats (B1; i.e., no infrastructure against cybersecurity attracts), health issues (B9; i.e., concerns on-screen time and cyber stress), and costly (B2; i.e., ICT infrastructure and fast-changing upgrades). ese findings draw parallel insights with recent studies concerning the readiness of the HEIs in developing economies. For example, Jamaludin et al. [4] raised concerns about the managerial and financial readiness of HEIs in the ASEAN countries. us, aside from the costs associated with EDUC4 implementation, the administrative aspect is essential in ensuring effective collaboration and dealing with apprehensive stakeholders. Another emerging literature emphasized that curriculum design for EDUC4 implementation must include teaching industrial cybersecurity to accelerate the next-generation programmers and cybersecurity researchers [50]. Lastly, Hariharasudan and Kot [51] emphasized the relevance of health issues following their observation that one of IoT's most critical industrial applications in the EDUC4 era includes medical, health, and elderly care. ese works in the literature justify the priority judgments of educational decision-makers at a university level from a developing economy perspective.
In addition, the decision-makers of the case HEI positioned insufficient foundation in basic education (B12; i.e., lack of learner's proper primary education), the complexity of learning platforms (B11; i.e., difficulty in utilizing virtual learning platforms), and time constraint for material preparation (B10; i.e., time constraint in preparation for virtual learning platform) among the minor priority barriers in achieving EDUC4. Unlike the other top priority barriers (i.e., B2, B9, B1, B6, and B4), the least three priorities barriers (i.e., B10, B11, and B10) are construed along with casespecific conditions of the HEI wherein limited or no control is available due to the trifocal education system [52] with each has own mandates and budgetary directions.  With this coordination, the connection between these government educational agencies shall see these gaps closed. On the other hand, B10 and B11 are deemed low-bearing barriers. For example, learning platforms are as common as social network sites (e.g., Google, LinkedIn, and Facebook). Educators have already integrated these sites as educational delivery tools in the learning environment. ese platforms are coined as an "alternative to the institutions' current Learning Management Systems (LMS)" in the delivery of asynchronous and synchronous learning [53]. LMS in HEIs is becoming responsive for organizing and distributing course materials. Since 2014, the case HEI has embarked on faculty development programs for the online LMS training and invested in the curriculum development and material preparation aligned with the LMS to make learning flexible and attuned to the requirements of EDUC4. us, the experts view these barriers with less priority. e use of the FF CODAS-SORT reveals the high-priority stakeholder roles in overcoming EDUC4 implementation barriers. For the government, these roles include the inclusion of cybersecurity awareness in the basic education curriculum (G3), allocating more funds to support the necessary inclusive activities in the implementation of EDUC4 (G4), designing the curricula in line with the implementation and sustainment of EDUC4 (G11), and streamlining alignment initiatives of the basic education agenda (e.g., human resources and curricula) to EDUC4 (G16). As pointed out in the domain literature, governments play a vital role in designing, implementing, and monitoring EDUC4. With regard to cybersecurity threats, the Philippine government, through its arms (i.e., CHED, DepEd, and TESDA), may promote the inclusion of cybersecurity awareness in the basic education curriculum to cater to such concerns. e CHED may organize a pool of experts to roam around the universities for such an agenda. On the other hand, allocating more funds to support the necessary inclusive activities in the implementation of EDUC4 is also encouraged by the government to cater to the skills gap of human capital, to add training resources, and also for the Philippines to catch up with the developed countries in terms of technological gaps. e Philippine government may also encourage its arms to design curricula that align with the implementation and sustainment of EDUC4. CHED shall strengthen the collaboration among its agencies to address the knowledge gap for the customization of curriculum design and insufficient foundation of basic education. is initiative may include retooling human resources (e.g., educators, educational managers, and ICT personnel) to bridge the complexity of learning platforms.
For the university managers, the high-priority roles include investing in efficient technologies (e.g., virtual classrooms, enablement or process audit, analytic tools for strategic planning, and the hybrid or fully automated process of project management), which are known to reduce overall costs and improve the experience of the university stakeholders (U19) and forging extensive collaboration with various stakeholders (e.g., policy-makers, academic experts, university networks, educators, education leaders, learners, and industry partners) to provide space and training  One efficient approach that is more applicable to the case HEI is to engage government institutions in finding collaborators as they can organize various stakeholders for an identified collaborative agenda. Nevertheless, the triple helix approach (i.e., government, industry, and academia) in initiating collaborations is rich in the literature (see [54]). For the human resource function, periodic training of the human resources on the skills (i.e., especially digital readiness and customization of curriculum design) fitting to the current demands of EDUC4 emerges as a high-priority role (H34). e HEI managers and their governing boards may work together to examine existing policies and guidelines in hiring teaching and non-teaching personnel to include the skills relevant to EDUC4 as part of the selection criteria. On the other hand, incumbent personnel could be submitted to rigorous training and seminars to transform the workforce into becoming EDUC4 ready. In this manner, the HEIs could effectively address the skill gap of the human capital barrier, particularly those related to the lack of skills  G1, G2, G5, G6, G7, G8,  G9, G10, G12, G13, G14,  G15, U17, U18, U20,  U21, U22, U23, U25,  U26, U27, H28, H29,  H30, H31, H32, H33,  H35, H36, H37, H38,  H39, I40, I41, I42, I43,  I44, E48, E49, E50, E51, E52, E53, E55 20 Complexity (B3) and training resources (B5). To make the training and seminars relevant and need-based, periodic inventories on personnel training needs and the timely response of the human resource personnel to the identified needs could help the HEIs retain the best and most qualified personnel while addressing the demands of EDUC4. Due to the danger primarily posed by online threats at the university level, educators can engage in continuous learning initiatives about relevant cybersecurity threats (i.e., data breaches on student information, denial of service attacks, and phishing; E45). is initiative will equip them with the necessary skills to help safeguard crucial information of learners and other members of the university. is may be achieved by integrating awareness of applicable laws to cyberbullying in (virtual) classroom teaching (E46). On the other hand, they can also devise alternative cost-efficient teaching strategies to deliver required learning outcomes geared to EDUC4 while upholding the implementation of EDUC4 (E47) and taking part in the design, development and improvement of innovative curricula aligned to EDUC4 (E54). Educators can also promote ways to efficiently prepare learning materials, including advanced ICTs (E56). ey can also participate in skills development initiatives to equip them with the capabilities in handling different complex learning platforms (E57).

Conclusion and Future Work
While the recent literature has identified barriers to implementing EDUC4 in developing economies, holistic insights into overcoming these barriers remain largely unknown. is gap poses the relevance of the roles of various stakeholders in generating insights for the design of strategies and initiatives in the implementation of EDUC4. In this work, designed for HEIs, an analytic evaluation tool based on integrating Fermatean fuzzy sets into a hybrid entropy-based CRITIC-CODAS-SORT for evaluating various stakeholder roles is proposed. With the entropy-based CRITIC assigning priority weights to the recently reported 12 barriers and the CODAS-SORT identifying those roles with high priority, the incorporation of FFS into the integrated methodology addresses epistemic uncertainties inherent in decision-making. rough a focus group discussion of experts on a case HEI in a developing economy, the roles of various stakeholders, including the government, university management, human resource, ICT function, and educators, were identified. e application of FF CRITIC yields the following most relevant barriers to EDUC4 implementation in developing economies: lack of collaboration, apprehensive stakeholders, cybersecurity threats, health issues, and costs.
To overcome these barriers, the proposed methodology finds the following high-priority stakeholder roles. e government must consider the inclusion of cybersecurity awareness in the basic education curriculum, allocating more funds to support the necessary inclusive activities in the implementation, designing the curricula in line with the implementation and sustainment of EDUC4, and streamlining alignment initiatives of the basic education agenda (e.g., human resources and curricula) to EDUC4 in its priority agenda. On the other hand, HEIs must invest in efficient technologies to reduce the overall costs of implementing EDUC4 and enhance the experience of university stakeholders. Also, they need to forge extensive collaboration with various stakeholders to provide the necessary resources for EDUC4 implementation. e human resource management function of HEIs must implement periodic training of educators on the skills required of EDUC4. Finally, educators have the highest number of critical roles, including engaging in continuous learning initiatives about relevant cybersecurity threats at the university; integrating awareness of applicable laws to cyberbullying in (virtual) classroom teaching; devising alternative cost-efficient teaching strategies in the delivery of required learning outcomes while upholding the implementation of EDUC4; taking part in the design, development, and improvement of innovative curricula aligned to EDUC4; promoting ways to efficiently prepare learning materials; including the use of advanced ICTs; and participating in skills development initiatives aimed at equipping educators with the capabilities in handling different complex learning platforms. e high-priority roles offer some insights into the design of specific initiatives in implementing EDUC4 in HEIs, not just in the case of university but in comparable HEIs, particularly in developing economies. Although idiosyncrasies exist, these insights may be relevant in other HEIs with similar conditions. Investigating how these roles or strategies may work out in practice is an interesting future endeavor and is highly suggested as a follow-up to this work. Furthermore, if available, the utilization of statistical data and analysis may be opted to cross-reference the findings of this study empirically. For instance, gathering data on the increase of utilization of digital technologies and other compositions of EDUC4 in different settings where some of these strategies are implemented may provide some idea on the actual effectiveness of the strategies, which can validate the results of this work based on expert decisions.

Data Availability
e perception data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.