# Fermatean Fuzzy DEMATEL and MMDE Algorithm for Modelling the Barriers of Implementing Education 4.0: Insights from the Philippines

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Method

#### 3.1. Preliminaries for the Computational Framework

- Fermatean Fuzzy Sets

**Definition**

**1**

**.**Let $X$ be a universe of discourse. The general form of an FFS, $\mathcal{F}$, in $X$ can be presented as:

**Definition**

**2**

**.**Let ${\mathcal{F}}_{i}=\left({\mu}_{{\mathcal{F}}_{i}}^{F},{\nu}_{{\mathcal{F}}_{i}}^{F}\right)$$\left(i=1,2,\dots ,n\right)$ be a set of FFS, and $w={\left({w}_{1},{w}_{2},\dots ,{w}_{n}\right)}^{T}$ be the corresponding weight vector such that $\sum _{i}{w}_{i}=1$. Then, the Fermatean fuzzy weighted average ($FFWA$) aggregation operator is defined by:

**Definition**

**3**

**.**Let $\mathcal{F}=\left({\mu}_{\mathcal{F}}^{F},{\nu}_{\mathcal{F}}^{F}\right)$ be an FFS. The score function ${S}^{F}$for $\mathcal{F}$ is defined as:

- Decision-Making Trial and Evaluation Laboratory

- Maximum Mean De-Entropy Algorithm

#### 3.2. Process Flow of the Proposed Computational Framework

**Step 1**: Identify the barriers to EDUC4 implementation. A list of barriers to implementing EDUC4 in HEIs can be constructed using a literature survey, interview with experts, or a focus group discussion.

**Step 2**: Set up the initial direct relation in FFS. From the list of barriers, decision-makers or experts are asked to elicit judgment on the degree of the causal relationship of each barrier to other barriers of EDUC4 implementation using a predefined scale. To capture the uncertainty and ambiguity within the dataset, a 5-point scale is provided with an equivalent linguistic evaluation scale and corresponding FFS values, as shown in Table 1.

**Step 3**: Aggregate the initial direct-relation matrices in FFS. To aggregate the initial direct-relation matrices, Equation (3) is used.

**Step 4**: Construct the corresponding crisp values of the initial direct-relation matrix. The initial direct-relation matrix in crisp values is calculated using Equation (4).

**Step 5**: Generate the normalized direct-relation matrix. The normalized direct-relation matrix is obtained using Equation (5) to Equation (7).

**Step 6**: Obtain the total relation matrix. The total relation matrix is obtained using Equation (8).

**Step 7**: Calculate the threshold value $\lambda $. The threshold value is determined via the MMDE algorithm detailed in Section 3.1.

**Step 8**: Construct the prominence-relation map using $\left(D+{R}^{T},D-{R}^{T}\right)$ coordinates, the components of which are obtained using Equations (9) and (10). The calculated threshold value $\lambda $ is used to filter out significant relationships among the barriers of EDUC4 implementation, and then a directed edge is drawn in the map.

#### 3.3. Case Study Background

#### 3.4. Data Gathering

## 4. Results and Discussion

#### 4.1. Baseline Results

#### 4.2. Policy Insights

#### 4.3. Scenario Analysis

## 5. Conclusions and Future Work

- The critical EDUC4 barriers in the baseline case are identified to be related to the lack of training resources (B5), costs (B2), insufficiency of available technologies (B8), skills gap of human resources (B3), knowledge gap (B7), and the complexity of the learning platforms (B11);
- The lack of training resources (B5) for implementing EDUC4 has the most influence on the other barriers, making it the most prominent dispatcher (in terms of frequency) in the baseline case;
- The complexity of learning platforms (B11) for EDUC4 implementation receives the most influence from the dispatchers, making it the most prominent receiver in the baseline case;
- The scenario analysis and the subsequent statistical test show that, while B5 is more prominent in terms of frequency of critical relationships with other EDUC4 barriers, addressing the cost barrier (B2) yields statistically more favorable results in terms of the general (mean) reduction of EDUC4 implementation barriers in the system.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Barriers to EDUC4 (adopted from Ref. [10]).

Code | Barrier | Brief Description |
---|---|---|

B1 | Cybersecurity threat | The threat of information leakage, security attacks, and misusage of technology. |

B2 | Costly | Implementation of EDUC4 is associated with higher costs (e.g., acquisition of equipment, maintenance). |

B3 | Skills gap of the human capital | Insufficient knowledge and experience of the human capital in using digital technology for education, including the lack of specific skills (i.e., critical thinking, emotional intelligence). |

B4 | Apprehensive stakeholders | Apprehension of some stakeholders (i.e., learners, educators, administrators) to EDUC4. |

B5 | Lack of training resources | The lack of training resources (i.e., facilities, materials) for the professional development of educators. |

B6 | Lack of collaboration | Lack of collaboration with other sectors (i.e., community, government, other HEIs, industry) is essential in successfully implementing EDUC4. |

B7 | Knowledge gap for the customization of curriculum design | Current lack of knowledge to create a customized curriculum design to enhance learners’ skills (i.e., creativity, critical thinking) and promote skills-based training. |

B8 | Insufficient available technologies | Due to the rapid advancement of technology, developing countries cannot catch up with the developed ones. Some technologies might be available in some countries, but not in others. |

B9 | Health issues | Prolonged exposure to the technology may cause health issues in the physical and mental well-being of the learners and educators. |

B10 | Time constraint for material preparation | Preparing and teaching in a virtual learning platform requires more time than the traditional one. |

B11 | Complexity of learning platforms | The challenge that the users (i.e., learners and educators) face on utilizing the virtual learning platform. |

B12 | Insufficient foundation in basic education | Quality primary education of learners is essential in the implementation of EDUC4 in HEIs. |

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Linguistic Variables | Influence Score | Equivalent FFSs |
---|---|---|

No Influence (NO) | 0 | $\left(0,1\right)$ |

Very Low (VL) | 1 | $\left(0.1,0.75\right)$ |

Low (L) | 2 | $\left(0.4,0.5\right)$ |

High (H) | 3 | $\left(0.7,0.2\right)$ |

Very High (VH) | 4 | $\left(0.9,0.1\right)$ |

Code | Barrier | $\mathit{D}$ | ${\mathit{R}}^{\mathit{T}}$ | $\left(\mathit{D}+{\mathit{R}}^{\mathit{T}}\right)$ | $\mathbf{Rank}\left(\mathit{D}+{\mathit{R}}^{\mathit{T}}\right)$ | $\left(\mathit{D}-{\mathit{R}}^{\mathit{T}}\right)$ | $\mathbf{Rank}\left(\mathit{D}-{\mathit{R}}^{\mathit{T}}\right)$ | Category |
---|---|---|---|---|---|---|---|---|

B1 | Cybersecurity threat | 6.35 | 6.00 | 12.35 | 10 | 0.35 | 5 | Net cause |

B2 | Costly | 7.06 | 6.38 | 13.43 | 5 | 0.68 | 1 | Net cause |

B3 | Skills gap of the human capital | 6.89 | 7.03 | 13.92 | 2 | −0.14 | 8 | Net effect |

B4 | Apprehensive stakeholders | 6.78 | 6.36 | 13.14 | 7 | 0.42 | 4 | Net cause |

B5 | Lack of training resources | 7.50 | 6.85 | 14.35 | 1 | 0.65 | 2 | Net cause |

B6 | Lack of collaboration | 6.77 | 6.19 | 12.95 | 9 | 0.58 | 3 | Net cause |

B7 | Knowledge gap for the customization of curriculum design | 6.43 | 6.90 | 13.33 | 6 | −0.47 | 9 | Net effect |

B8 | Insufficient available technologies | 6.93 | 6.97 | 13.90 | 3 | −0.03 | 7 | Net effect |

B9 | Health issues | 5.19 | 5.80 | 10.98 | 12 | −0.61 | 11 | Net effect |

B10 | Time constraint for material preparation | 6.26 | 6.80 | 13.06 | 8 | −0.54 | 10 | Net effect |

B11 | Complexity of learning platforms | 6.30 | 7.43 | 13.73 | 4 | −1.14 | 12 | Net effect |

B12 | Insufficient foundation in basic education | 6.29 | 6.03 | 12.32 | 11 | 0.26 | 6 | Net cause |

Item | Data |
---|---|

$\mathrm{The}\mathrm{ordered}\mathrm{triplet}\mathrm{set},{T}^{*}$ | $\left\{\begin{array}{c}\left(0.71,5,11\right),\left(0.68,5,8\right),\left(0.67,5,3\right),\left(0.67,2,11\right),\left(0.66,8,11\right),\\ \left(0.66,3,11\right),\left(0.66,5,7\right),\left(0.66,5,10\right),\left(0.65,6,11\right),\dots ,\left(0.34,9,9\right)\end{array}\right\}$ |

$\mathrm{Dispatch}-\mathrm{node}\mathrm{set},{T}^{Di}$ | $\left\{5,5,5,2,8,3,5,5,6,\dots ,9\right\}$ |

${T}_{i}^{Di}$$\mathrm{sets}\mathrm{and}MD{E}_{i}^{Di}$ values | $\begin{array}{l}{T}_{1}^{Di}=\left\{5\right\},MD{E}_{1}^{Di}=0;{T}_{2}^{Di}=\left\{5,5\right\},MD{E}_{2}^{Di}=0;{T}_{3}^{Di}=\left\{5,5,5\right\},\\ MD{E}_{3}^{Di}=0;{T}_{4}^{Di}=\left\{5,5,5,2\right\},MD{E}_{4}^{Di}=0.028;\dots \end{array}$ |

$\mathrm{Set}\mathrm{of}MD{E}_{i}^{Di}$ values | $\left\{0,0,0,0.028,0.021,0.016,0.025,0.034,0.027,\dots ,0\right\}$ |

$\mathrm{Maximum}MD{E}_{i}^{Di}$ | $0.034$ |

$\mathrm{Dispatch}-\mathrm{node}\mathrm{set}\mathrm{of}\mathrm{the}\mathrm{maximum}MD{E}_{i}^{Di}$ | $\left\{5,2,8,3\right\}$ |

$\mathrm{Receive}-\mathrm{node}\mathrm{set},{T}^{Re}$ | $\left\{11,8,3,11,11,11,7,10,11,\dots ,9\right\}$ |

$\mathrm{Set}\mathrm{of}MD{E}_{i}^{Re}$ values | $\left\{0,0,0,0.009,0.021,0.033,0.025,0.019,0.027,\dots ,0\right\}$ |

$\mathrm{Maximum}MD{E}_{i}^{Re}$ | $0.033$ |

$\mathrm{Receive}-\mathrm{node}\mathrm{set}\mathrm{of}\mathrm{the}\mathrm{maximum}MD{E}_{i}^{Re}$ | $\left\{11,8,3\right\}$ |

${T}_{max}^{Di}$ | $\left\{\left(0.71,5,11\right),\left(0.67,2,11\right),\left(0.66,8,11\right),\left(0.66,3,11\right)\right\}$ |

${T}_{max}^{Re}$ | $\left\{\left(0.71,11,5\right),\left(0.68,8,5\right),\left(0.67,3,5\right)\right\}$ |

${T}^{Th}$ | $\left\{\begin{array}{c}\left(0.71,5,11\right),\left(0.67,2,11\right),\left(0.66,8,11\right),\left(0.66,3,11\right),\\ \left(0.71,11,5\right),\left(0.68,8,5\right),\left(0.67,3,5\right)\end{array}\right\}$ |

$\mathrm{Threshold}\mathrm{value}\left(\lambda \right)$ | $0.66$ |

**Table 4.**The t-test assuming unequal variances of comparisons of the mean of the total relation matrices for the baseline, scenario (a), and scenario (b).

Baseline | Scenario (a) | Baseline | Scenario (b) | Scenario (a) | Scenario (b) | |
---|---|---|---|---|---|---|

Mean | 0.5430 | 0.3338 | 0.5273 | 0.4333 | 0.3338 | 0.4333 |

Variance | 0.0042 | 0.0019 | 0.0057 | 0.0030 | 0.0019 | 0.0030 |

Observations | 132 | 132 | 132 | 132 | 132 | 132 |

df | 230 | 238 | 251 | |||

t Stat | 30.7897 | 11.5844 | −16.3662 | |||

p-value (two-tail) | 0.0000 * | 0.0000 * | 0.0000 * | |||

t Critical (two-tail) | 1.9703 | 1.9700 | 1.9695 |

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Gonzales, G.; Costan, F.; Suladay, D.; Gonzales, R.; Enriquez, L.; Costan, E.; Atibing, N.M.; Aro, J.L.; Evangelista, S.S.; Maturan, F.;
et al. Fermatean Fuzzy DEMATEL and MMDE Algorithm for Modelling the Barriers of Implementing Education 4.0: Insights from the Philippines. *Appl. Sci.* **2022**, *12*, 689.
https://doi.org/10.3390/app12020689

**AMA Style**

Gonzales G, Costan F, Suladay D, Gonzales R, Enriquez L, Costan E, Atibing NM, Aro JL, Evangelista SS, Maturan F,
et al. Fermatean Fuzzy DEMATEL and MMDE Algorithm for Modelling the Barriers of Implementing Education 4.0: Insights from the Philippines. *Applied Sciences*. 2022; 12(2):689.
https://doi.org/10.3390/app12020689

**Chicago/Turabian Style**

Gonzales, Gamaliel, Felix Costan, Decem Suladay, Roselyn Gonzales, Lynne Enriquez, Emily Costan, Nadine May Atibing, Joerabell Lourdes Aro, Samantha Shane Evangelista, Fatima Maturan,
and et al. 2022. "Fermatean Fuzzy DEMATEL and MMDE Algorithm for Modelling the Barriers of Implementing Education 4.0: Insights from the Philippines" *Applied Sciences* 12, no. 2: 689.
https://doi.org/10.3390/app12020689