**Effective Ways to Prevent COVID-19 From Spreading Using Fuzzy Analytic** **Hierarchy** **Process** **(AHP) Method**
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**HIGHLIGHTS**
- *The* Fuzzy Analytic Hierarchy Process *(FAHP) method was used to select the effective ways to prevent COVID-19 from spreading.*
- There are seven strategies listed for COVID-19 prevention and evaluated by three experts in their respective fields as decision makers.
- The Fuzzy AHP approach simply converts the AHP scale into a fuzzy triangle scale that can be accessed first.
**ABSTRACT**
*The spread of coronavirus disease 2019* *(COVID-19)* *has resulted in numerous economic and social damages. Malaysia is one of the countries that were badly* *affected* *by COVID-19. The ability* *of* *coronavirus spreading directly from one person to another has* *led* *to* *the* *rapid* *daily* *increase* *in number* *of* *case of COVID-19* *in Malaysia even though the government has* *taken many actions to prevent the virus from spreading. This study aims to select effective ways to prevent COVID-19 in Malaysia using the Fuzzy Analytic Hierarchy Process (FAHP) method. An analytical study was conducted between three decision-makers which are a nurse, a Medical Officer (MO), and a Medical Assistant (MA) to determine the impact of these preventive measures (e.g.,social/physica* *measuresl, health monitoring, unnecessary touching of* *things, hygiene, immunity/fitness, healthy diet, and sharing personal items) on COVID-19. There are eight steps in the FAHP method that can effectively achieved the objective of this study. The findings of this study shows* *that hygiene* *is important* *in preventing the spreading of COVID-19. Wearing a mask can also* *help prevent* *its* *spread to others.* *Next* *to touching public objects* *comes, always washing or sanitizing* *one’s hands and covering* *one’s coughs and sneezes.*
***Keywords:** COVID-19, effective* *measures, FAHP, select, spread*
# INTRODUCTION
**The world has become infected with coronavirus disease 2019 (COVID-19), which is caused by coronavirus 2 that causes severe acute respiratory syndrome coronavirus** **2** **(SARS-CoV-2). Based on a study by** **Pazos (2020), the first cases** **was discovered in Wuhan, Hubei province, when employees at the Huanan Wholesale Seafood Market, which sold seafood, poultry, and birds, became ill with mysterious pneumonia, once again linking wild animal markets to** **severe acute respiratory syndrome** **(SARS). Then, China notified the World Health Organization (WHO) about the sequence of instances for the first time on 31** **December** **, 2019, 23 days after the first patient sought medical treatment.**
# Subsequently, WHO then declared COVID-19 a global pandemic. According to WHO (2020), the conference was convened following WHO Director-General Dr. Tedros Adhanom Ghebreyesus' announcement that COVID-19 can be designated a pandemic. This is due to a sharp increase in the number of cases outside of China in the last two weeks, affecting an expanding number of nations. In addition, clusters of cases or population transmission are becoming more common in several countries, according to Dr. Hans Henri P. Kluge, WHO Regional Director for Europe. He anticipates that the number of cases and deaths will continue to increase steadily in the days and weeks ahead and that we will need to ramp up our response to take pre-emptive measures wherever possible. Such measures can help postpone the outbreak, allowing healthcare systems more time to plan for the effect and assimilate it.
# Moreover, Malaysia is also one of the countries that have been affected by the novel coronavirus. The first coronavirus cases were confirmed among three Chinese nationals who were quarantined at Sungai Buloh Hospital. The three were among eight Chinese nationals who were quarantined in a hotel in Johor Bahru, according to former Health Minister Datuk Seri Dr. Dzulkefly Ahmad. They were taken to Sungai Buloh Hospital for further treatment. The three are also alleged to be in the vicinity of a 66-year-old Singapore patient who has tested positive for the virus. This is the country's first reported identification of the novel coronavirus, also known as 2019-nCoV (Ting, 2020).
# Therefore, in collaboration with the Ministry of Health (MoH), the Malaysian government has put in a lot of effort to face and deal with the outbreak situation (Shah et al., 2020). The next important measure taken by the MoH and the government to combat COVID-19 spread was to expand the number of facilities equipped to handle COVID-19 cases. To accommodate the growing number of infection cases, public and private institutions, including university hospitals and Ministry of Defense hospitals, collaborated (The Edge Markets, 2020).
# However, this paper discusses the study on selecting the effective ways to prevent COVID-19 from spreading using the Fuzzy Analytic Hierarchy Process (AHP) Method. Based on the study by Putra et al. (2018), the Fuzzy AHP is a fuzzy logic-based Analytic Hierarchy Process (AHP) approach. This study is limited to the prevention strategies in Malaysia. The Fuzzy AHP approach is comparable to the AHP approach, which simply converts the AHP scale into a fuzzy triangle scale that can be accessed first.
# METHODOLOGY
The Fuzzy Analytic Hierarchy Process (FAHP) is an Analytic Hierarchy Process (AHP) technique based on fuzzy logic. The AHP method is comparable to the FAHP methodology. The FAHP approach simply converts the AHP scale into a fuzzy triangle scale that can be accessed first (Putra et al., 2018). Although FAHP contains several other strategies, the relative relevance weights for the criteria in this study are estimated using Buckley's approach (Ayhan, 2013). Several steps in the technique are as follows:
**Step 1:** The criteria or alternatives are compared by decision-maker (DM) using the linguistic terms indicated in Table 1.
**Table 1:** Linguistic terms and the corresponding triangular fuzzy numbers.
| | | |
| --------------- | --------------------------------------------------- | -------------------------- |
| **Saaty scale** | **Definition** | **Fuzzy Triangular Scale** |
| 1 | Equally important (Eq. Imp.) | (1, 1, 1) |
| 3 | Weakly important (W. Imp.) | (2, 3, 4) |
| 5 | Fairly important (F. Imp.) | (4, 5, 6) |
| 7 | Strongly important (S. Imp.) | (6, 7, 8) |
| 9 | Absolutely important (A. Imp.) | (9, 9, 9) |
| 2 | The intermittent values between two adjacent scales | (1, 2, 3) |
| 4 | | (3, 4, 5) |
| 6 | | (5, 6, 7) |
| 8 | | (7, 8, 9) |
As an example, if the decision-maker declares that "Criterion 1 (C1) is Weakly Important than Criterion 2 (C2)", the fuzzy triangular scale is taken as "Criterion 1 (C1) is Weakly Important than Criterion 2 (C2)", (2, 3, 4). In the pair-wise contribution matrix of the criterion, on the contrary, the comparison of C2 to C1 will be made on a fuzzy triangular scale of (1/4, 1/3, 1/2) (Ayhan, 2013).
The pair-wise contribution matrix is illustrated in Eq.1, where \(\widetilde{d_{\text{ij}}^{k}}\) denotes the kth the preference of the decision-maker for the ith criterion over the jth criterion, expressed as fuzzy triangular numbers. In this situation, “tilde” denotes the triangular number demonstration, and \(\widetilde{d_{12}^{1}}\) denotes the first preference of decision-maker for the first criterion takes priority over the second and equals \(\widetilde{d_{12}^{1}}\) = (2,3,4).
\(\widetilde{A^{k}\ }\) = \(\begin{bmatrix}
\widetilde{d_{11}^{k}} & \widetilde{d_{12}^{k}} & \ldots & \widetilde{d_{1n}^{k}} \\
\widetilde{d_{21}^{k}} & \ldots & \ldots & \widetilde{d_{2n}^{k}} \\
\ldots & \ldots & \ldots & \ldots \\
\widetilde{d_{n1}^{k}} & \widetilde{d_{n2}^{k}} & \ldots & \widetilde{d_{\text{nn}}^{k}} \\
\end{bmatrix}.\) (1)
**Step 2:** Check the consistency (CR – consistency ratio).
The consistency of an evaluation was examined using the formula below to ensure the expert's consistent judgement.
\(CI = \ \frac{\lambda_{\max} - N}{N - 1}\) . (2)
Here, \(\text{CI}\) is the Consistency Index, \(\lambda_{\max}\) is the largest eigenvalue of the comparison matrix, and N is the dimension of the matrix/number of criteria.
\(CR = \ \frac{\text{CI}}{\text{RI}}\) . (3)
Table 2 below shows the random inconsistency indices \((RI)\) (Saaty, 1980).
**Table 2:** Random Inconsistency Indices \((RI)\).
| | | | | | | | | | | |
| -- | - | - | ---- | --- | ---- | ---- | ---- | ---- | ---- | ---- |
| N | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| RI | 0 | 0 | 0.58 | 0.9 | 1.12 | 1.24 | 1.32 | 1.41 | 1.46 | 1.49 |
**Step 3:** If there are many DM, the preferences of each \((\widetilde{d_{\text{ij}}^{k})}\) are averaged, while (\(\widetilde{d_{\text{ij}}}\)) is determined as in Eq.4.
\(\widetilde{d_{\text{ij}}}\) = \(\frac{\sum_{k - 1}^{k}\widetilde{d_{\text{ij}}^{k}}}{K}\) . (4)
**Step 4:** As indicated in Eq.5, the pair-wise contribution matrix is updated based on averaged preferences.
\(\widetilde{A}\) = \(\begin{bmatrix}
\widetilde{d_{11}} & \cdots & \widetilde{d_{1n}} \\
\vdots & \ddots & \vdots \\
\widetilde{d_{n1}} & \cdots & \widetilde{d_{\text{nn}}} \\
\end{bmatrix}.\) (5)
**Step 5:** Buckley (1985) states that the geometric mean of each criterion's fuzzy comparison values is obtained as stated in Eq.6. Here, \(\widetilde{r_{i}}\) stands for triangular values in this case.
\(\widetilde{r_{i}}\) = \(\left( \prod_{j = 1}^{n}\widetilde{d_{\text{ij}}} \right)^{\frac{1}{n}}\) , \(i = 1,\ 2,\ldots,\ n\) . (6)
**Step 6:** By adding the next three substages to Eq.7, the fuzzy weights of each criterion may be found.
i) Find each \(\widetilde{r_{i}}\) vector summation.
ii) Find the summation vector's (-1) power. To make it in ascending order, remove the fuzzily triangular number.
iii) Multiply each \(\widetilde{r_{i}}\) by this reverse vector to get the fuzzy weight of criterion i \(\left( \widetilde{w_{i}} \right)\).
\(\widetilde{w_{i}} = \ \widetilde{r_{i}}\ \bigotimes\ {(\widetilde{r_{1}}\ \bigoplus\widetilde{r_{2}}\bigoplus\cdots\bigoplus\widetilde{r_{n}})}^{- 1}\),
\(= \left( \text{lw}_{i},\ \text{mw}_{i},\ \text{uw}_{i} \right).\) (7)
**Step 7:** \(\widetilde{w_{i}}\) must be defuzzified using the Centre of Area method because they are still fuzzy triangular numbers Eq.8.
\(M_{i} = \ \frac{\text{lw}_{i} + \ \text{mw}_{i} + \text{uw}_{i}}{3}\) . (8)
**Step 8:** \(M_{i}\) is not a fuzzy number. Nevertheless, it must be normalized using Eq.9.
\(N_{i} = \frac{M_{i}}{\sum_{i = 1}^{n}M_{i}}\) . (9)
The normalized weights of criterion are determined using these eight procedures. The decision-maker is recommended the option with the highest score based on these results (Ayhan, 2013).
**Application of Fuzzy AHP on COVID-19 Prevention Strategies**
This study needs to define the problem according to the criteria used to select the prevention strategies. The main criteria for selecting prevention strategies are social/physical, health monitoring, unnecessary touching things, hygiene, immunity/fitness, healthy diet, and sharing personal items. The criteria weights should be calculated at this point. Thus, the criteria will be calculated using the step stated above. Figure 1 shows the criteria of the prevention strategies.
**Figure 1:** Criteria of COVID-19 Prevention Strategies.
**FINDINGS AND DISCUSSIONS**
The FAHP has been used to the best of its ability to determine highly effective COVID-19 preventative measures. Three professionals in the field, including a nurse from Klinik Batu 10 Lekir, Perak, Malaysia, a Medical Officer (MO) from Kementerian Kesihatan Malaysia (KKM), and a Medical Assistant (MA) from Hospital Jelebu, Negeri Sembilan, Malaysia, were surveyed. This strategy is used to weigh the criteria employed in this selection procedure. In the following Table 3, the acronyms for each criterion utilized in this study are listed:
**Table 3:** Acronym of each criterion.
| | |
| ------------ | --------------------------- |
| **CRITERIA** | **DESCRIPTION** |
| SP | Social/Physical |
| HM | Health monitor |
| UT | Unnecessary touching things |
| H | Hygiene |
| IF | Immunity/Fitness |
| HD | Healthy diet |
| SI | Sharing personal items |
**Determining the Weights of Criteria**
A conference with three specialists is held to select the most suitable applicant. Three decision-makers (DM) participate in the evaluation process, and a question form is issued to each of them, based on the hierarchy of selecting effective ways to prevent COVID-19 from spreading that has been developed in Figure 1. Then, using fuzzy triangular numbers that show the relative strength of each pair of components in the same hierarchy, pair-wise comparisons are created for each criterion.
The pair-wise comparison of the criteria from each DM was produced based on their preferences. Therefore, according to the three tables above, the pair-wise comparison matrices for criterion are provided in Tables 4, 5, and 6. The values are based on the fuzzy triangular scale, as indicated in Table 1.
**Table 4:** Comparison matrices of criteria for decision-maker 1 (\(\widetilde{d^{1}}\)).
| | | | | | | | |
| ------------ | --------------- | --------------- | --------------- | --------------- | --------------- | --------- | --------------- |
| **CRITERIA** | **SP** | **HM** | **UT** | **H** | **IF** | **HD** | **SI** |
| **SP** | (1, 1, 1) | (1, 1, 1) | (2, 3, 4) | (1, 1, 1) | (4, 5, 6) | (9, 9, 9) | (1, 1, 1) |
| **HM** | (1, 1, 1) | (1, 1, 1) | (4, 5, 6) | (1, 1, 1) | (4, 5, 6) | (9, 9, 9) | (1, 1, 1) |
| **UT** | (1/4 ,1/3 ,1/2) | (1/6, 1/5, 1/4) | (1, 1, 1) | (1/4, 1/3, 1/2) | (4, 5, 6) | (4, 5, 6) | (1/4, 1/3, 1/2) |
| **H** | (1, 1, 1) | (1, 1, 1) | (2, 3, 4) | (1, 1, 1) | (4, 5, 6) | (9, 9, 9) | (1, 1, 1) |
| **IF** | (1/6, 1/5, 1/4) | (1/6, 1/5, 1/4) | (1/6, 1/5, 1/4) | (1/6, 1/5, 1/4) | (1, 1, 1) | (4, 5, 6) | (1/6, 1/5, 1/4) |
| **HD** | (1/9, 1/9, 1/9) | (1/9, 1/9, 1/9) | (1/6, 1/5, 1/4) | (1/9, 1/9, 1/9) | (1/6, 1/5, 1/4) | (1, 1, 1) | (1/9, 1/9, 1/9) |
| **SI** | (1, 1, 1) | (1, 1, 1) | (2, 3, 4) | (1, 1, 1) | (4, 5, 6) | (9, 9, 9) | (1, 1, 1) |
**Table 5:** Comparison matrices of criteria for decision-maker 2 (\(\widetilde{d^{2}}\)).
| | | | | | | | |
| ------------ | --------------- | --------------- | --------------- | --------------- | --------- | --------------- | --------------- |
| **CRITERIA** | **SP** | **HM** | **UT** | **H** | **IF** | **HD** | **SI** |
| **SP** | (1, 1, 1) | (1, 1, 1) | (2, 3, 4) | (1/4, 1/3, 1/2) | (9, 9, 9) | (2, 3, 4) | (2, 3, 4) |
| **HM** | (1, 1, 1) | (1, 1, 1) | (2, 3, 4) | (1/6, 1/5, 1/4) | (9, 9, 9) | (4, 5, 6) | (2, 3, 4) |
| **UT** | (1/4 ,1/3 ,1/2) | (1/4 ,1/3 ,1/2) | (1, 1, 1) | (1/8, 1/7, 1/6) | (6, 7, 8) | (4, 5, 6) | (1, 1, 1) |
| **H** | (2, 3, 4) | (4, 5, 6) | (6, 7, 8) | (1, 1, 1) | (9, 9, 9) | (9, 9, 9) | (4, 5, 6) |
| **IF** | (1/9, 1/9, 1/9) | (1/9, 1/9, 1/9) | (1/8, 1/7, 1/6) | (1/9, 1/9, 1/9) | (1, 1, 1) | (1/4, 1/3, 1/2) | (1/6, 1/5, 1/4) |
| **HD** | (1/4, 1/3, 1/2) | (1/6, 1/5, 1/4) | (1/6, 1/5, 1/4) | (1/9, 1/9, 1/9) | (2, 3, 4) | (1, 1, 1) | (1/4, 1/3, 1/2) |
| **SI** | (1/4, 1/3, 1/2) | (1/4, 1/3, 1/2) | (1, 1, 1) | (1/6, 1/5, 1/4) | (4, 5, 6) | (2, 3, 4) | (1, 1, 1) |
**Table 6:** Comparison matrices of criteria for decision-maker 3 (\(\widetilde{d^{3}}\)).
| | | | | | | | |
| ------------ | --------------- | --------------- | --------------- | --------------- | --------- | --------------- | --------------- |
| **CRITERIA** | **SP** | **HM** | **UT** | **H** | **IF** | **HD** | **SI** |
| **SP** | (1, 1, 1) | (2, 3, 4) | (4, 5, 6) | (1, 1, 1) | (9, 9, 9) | (6, 7, 8) | (2, 3, 4) |
| **HM** | (1/4 ,1/3 ,1/2) | (1, 1, 1) | (4, 5, 6) | (1/4 ,1/3 ,1/2) | (6, 7, 8) | (2, 3, 4) | (1, 1, 1) |
| **UT** | (1/6, 1/5, 1/4) | (1/6, 1/5, 1/4) | (1, 1, 1) | (1/6, 1/5, 1/4) | (2, 3, 4) | (2, 3, 4) | (1/4, 1/3, 1/2) |
| **H** | (1, 1, 1) | (2, 3, 4) | (4, 5, 6) | (1, 1, 1) | (9, 9, 9) | (6, 7, 8) | (2, 3, 4) |
| **IF** | (1/9, 1/9, 1/9) | (1/8, 1/7, 1/6) | (1/4 ,1/3 ,1/2) | (1/9, 1/9, 1/9) | (1, 1, 1) | (1/6, 1/5, 1/4) | (1/8, 1/7, 1/6) |
| **HD** | (1/8, 1/7, 1/6) | (1/4 ,1/3 ,1/2) | (1/4 ,1/3 ,1/2) | (1/8, 1/7, 1/6) | (4, 5, 6) | (1, 1, 1) | (1/6, 1/5, 1/4) |
| **SI** | (1/4, 1/3, 1/2) | (1, 1, 1) | (2, 3, 4) | (1/4 ,1/3 ,1/2) | (6, 7, 8) | (4, 5, 6) | (1, 1, 1) |
The consistency of an evaluation was examined using Eq.1 and Eq.2 to ensure the expert's consistent judgment.
The comparison is permitted if consistency ratio (CR) is equal to or less than 0.1. When the CR value is larger than 0.1, it indicates that the judgment is inconsistent. An example calculation for the consistency ratio of the decision-maker 1 is as follows.
Pair-wise comparison matrix for criteria of decision-maker 1,
\(A = \begin{bmatrix}
1 & 1 & 3 & 1 & 5 & 9 & 1 \\
1 & 1 & 5 & 1 & 5 & 9 & 1 \\
\frac{1}{3} & \frac{1}{5} & 1 & \frac{1}{3} & 5 & 5 & \frac{1}{3} \\
1 & 1 & 3 & 1 & 5 & 9 & 1 \\
\frac{1}{5} & \frac{1}{5} & \frac{1}{5} & \frac{1}{5} & 1 & 5 & \frac{1}{5} \\
\frac{1}{9} & \frac{1}{9} & \frac{1}{5} & \frac{1}{9} & \frac{1}{5} & 1 & \frac{1}{9} \\
1 & 1 & 3 & 1 & 5 & 9 & 1 \\
\end{bmatrix}\),
\(\lambda_{\max} = 7.3458\),
\[CI = \frac{7.3458 - 7}{7 - 1} = 0.0576,\]
\[CR = \frac{0.0576}{1.32} = 0.0437 < 0.1.\]
For the Decision-Maker 2 and Decision-Maker 2, their CR are 0.06 and \(0.0586\) respectively.
Since the CR of each decision-maker is less than 0.1, the comparison is acceptable.
Then, the average of three decision-makers preferences \(({\widetilde{d}}_{\text{ij}}^{k})\) is determined, and \(({\widetilde{d}}_{\text{ij}})\) is calculated as indicated follow.
\({\widetilde{d}}_{\text{ij}} = \left( \frac{{{\widetilde{d}}^{1}}_{\text{ij}} + {{\widetilde{d}}^{2}}_{\text{ij}} + {{\widetilde{d}}^{3}}_{\text{ij}}}{3},\frac{{{\widetilde{d}}^{1}}_{\text{ij}} + {{\widetilde{d}}^{2}}_{\text{ij}} + {{\widetilde{d}}^{3}}_{\text{ij}}}{3},\frac{{{\widetilde{d}}^{1}}_{\text{ij}} + {{\widetilde{d}}^{2}}_{\text{ij}} + {{\widetilde{d}}^{3}}_{\text{ij}}}{3},\frac{{{\widetilde{d}}^{1}}_{\text{ij}} + {{\widetilde{d}}^{2}}_{\text{ij}} + {{\widetilde{d}}^{3}}_{\text{ij}}}{3},\frac{{{\widetilde{d}}^{1}}_{\text{ij}} + {{\widetilde{d}}^{2}}_{\text{ij}} + {{\widetilde{d}}^{3}}_{\text{ij}}}{3},\ \ \frac{{{\widetilde{d}}^{1}}_{\text{ij}} + {{\widetilde{d}}^{2}}_{\text{ij}} + {{\widetilde{d}}^{3}}_{\text{ij}}}{3},\frac{{{\widetilde{d}}^{1}}_{\text{ij}} + {{\widetilde{d}}^{2}}_{\text{ij}} + {{\widetilde{d}}^{3}}_{\text{ij}}}{3}\ \right).\) (10)
Table 7 shows a table of each decision-maker's average choice of criterion based on the computations using Eq.10 above.
**Table 7:** Average Preference of Criteria of each decision-maker.
| | | | | | | | |
| ------------ | ------------------ | ------------------ | ------------------ | ------------------ | ------------------ | ------------------ | ------------------ |
| **CRITERIA** | **SP** | **HM** | **UT** | **H** | **IF** | **HD** | **SI** |
| **SP** | (1, 1, 1) | (1.33, 1.67, 2) | (2.67, 3.67, 4.67) | (0.75, 0.78, 0.83) | (7.33, 7.67, 8) | (5.67, 6.33, 7) | (1.67, 2.33, 3) |
| **HM** | (0.75, 0.78, 0.83) | (1, 1, 1) | (3.33, 4.33, 5.33) | (0.47, 0.51, 0.58) | (6.33, 7, 7.67) | (5, 5.67, 6.33) | (1.33, 1.67, 2) |
| **UT** | (0.22 ,0.29 ,0.42) | (0.19, 0.24, 0.33) | (1, 1, 1) | (0.18, 0.23, 0.31) | (4, 5, 6) | (3.33, 4.33, 5.33) | (0.5, 0.56, 0.67) |
| **H** | (1.33, 1.67, 2) | (2.33, 3, 3.67) | (4, 5, 6) | (1, 1, 1) | (7.33, 7.67, 8) | (8, 8.33, 8.67) | (2.33, 3, 3.67) |
| **IF** | (0.13, 0.14, 0.16) | (0.13, 0.15, 0.18) | (0.18, 0.23, 0.31) | (0.11, 0.11, 0.11) | (1, 1, 1) | (1.47, 1.84, 2.25) | (0.15, 0.18, 0.22) |
| **HD** | (0.16, 0.2, 0.26) | (0.18, 0.21, 0.29) | (0.19, 0.24, 0.33) | (0.12, 0.12, 0.13) | (2.06, 2.73, 3.42) | (1, 1, 1) | (0.18, 0.21, 0.29) |
| **SI** | (0.5, 0.56, 0.67) | (0.75, 0.78, 0.83) | (1.67, 2.33, 3) | (0.47, 0.51, 0.58) | (4.67, 5.67, 6.67) | (5, 5.67, 6.33) | (1, 1, 1) |
Eq.6 is used to get the geometric mean of fuzzy comparison values of each criterion once the first three steps of the process have been completed. For instance, \(\widetilde{r_{i}}\) given in Eq.11 is used to find the geometric mean of fuzzy comparison values for the criterion.
\(\widetilde{r_{i}}\) = \(\left( \prod_{j = 1}^{n}\widetilde{d_{\text{ij}}} \right)^{\frac{1}{n}}\) (11)
\= \[\(({1 \ast 1.33 \ast 2.67 \ast 0.75 \ast 7.33 \ast 5.67 \ast 1.67)\ }^{\frac{1}{7}}\); \({(1 \ast 1.67 \ast 3.67 \ast 0.78 \ast 7.67 \ast 6.33 \ast 2.33)}^{\frac{1}{7}}\); \({(1 \ast 2 \ast 4.67 \ast 0.83 \ast 8 \ast 7 \ast 3)}^{\frac{1}{7}}\)\]
\= \[2.108; 2.456; 2.787\].
As a result, Table 8 displays the geometric means of fuzzy comparison values for all criteria. The total values, as well as the reverse values, are also shown. The arrangement of the numbers in the last row of Table 8 has been modified because the fuzzy triangular number should be in increasing order.
**Table 8:** Geometric means of fuzzy comparison values of criteria.
| | | | |
| ------------ | ---------------------------------- | ------ | ------ |
| **CRITERIA** | **GEOMETRIC MEAN OF FUZZY (r*i*)** | | |
| SP | 2.108 | 2.456 | 2.787 |
| HM | 1.748 | 1.967 | 2.203 |
| UT | 0.656 | 0.790 | 0.986 |
| H | 2.895 | 3.356 | 3.788 |
| IF | 0.259 | 0.291 | 0.335 |
| HD | 0.303 | 0.357 | 0.439 |
| SI | 1.317 | 1.493 | 1.700 |
| | | | |
| **Total** | 9.285 | 10.709 | 12.238 |
| **P (-1)** | 0.108 | 0.093 | 0.082 |
| **INCR** | 0.082 | 0.093 | 0.108 |
The fuzzy weight of the criterion \((\widetilde{w_{i})}\) is obtained in the fifth phase using Eq.7 and indicated in Eq.12.
\(w_{i}\) = \[\(\left( 2.108 \ast 0.082 \right);\left( 2.456 \ast 0.093 \right);(2.787 \ast 0.108)\)\] (12)
\= \[0.172; 0.229; 0.300\].
As a result, Table 9 shows the relative fuzzy weights of each criterion.
**Table 9:** Relative fuzzy weights of the criteria.
| | | | |
| ------------ | ----------------------- | ----- | ----- |
| **CRITERIA** | **FUZZY WEIGHT (w*i*)** | | |
| SP | 0.172 | 0.229 | 0.300 |
| HM | 0.143 | 0.184 | 0.237 |
| UT | 0.054 | 0.074 | 0.106 |
| H | 0.237 | 0.313 | 0.408 |
| IF | 0.021 | 0.027 | 0.036 |
| HD | 0.025 | 0.033 | 0.047 |
| SI | 0.108 | 0.139 | 0.183 |
Taking the average of fuzzy numbers for each criterion, the relative non-fuzzy weight of each criterion \({(M}_{i})\) is derived in the sixth step. The normalized weights of each criterion are generated and summarized in Table 10 in the seventh phase, using non-fuzzy \(M_{i}\)'s.
**Table 10:** Averaged and normalized relative weights of the criteria.
| | | | |
| ------------ | ---------------------------------- | ------------------------------------ | -------- |
| **CRITERIA** | **Averaged weight criterion (Mi)** | **Normalized weight criterion (Ni)** | **Rank** |
| SP | 0.234 | 0.228 | 2 |
| HM | 0.188 | 0.183 | 3 |
| UT | 0.078 | 0.076 | 5 |
| H | 0.319 | 0.311 | 1 |
| IF | 0.028 | 0.027 | 7 |
| HD | 0.035 | 0.034 | 6 |
| SI | 0.143 | 0.140 | 4 |
As a result, hygiene (H) has the highest normalized relative weights value of 0.311, according to the table 10. This number indicates that H has the biggest contribution in selecting effective ways to prevent COVID-19 from spreading. As we know, wearing a mask is mandatory for everyone when doing outdoor activities. Wearing a mask can prevent transferring the virus to another person. Then, always wash or sanitize hands after touching public objects and cover cough and sneezes.
The second higher normalization relative weight is social/physical (SP), which is 0.228. Therefore, a movement Control Order (MCO) was required when the COVID-19 infection rate reached a critical level. Furthermore, avoiding crowded places and practicing 1-meter social distancing can prevent COVID-19 from spreading.
Health monitor (HM) is the third higher which is 0.183. Before entering public places such as super-market, restaurants, mosques, etc., screening temperature is required. Anyone who has had close contact with someone who has COVID-19 should be in quarantine for 14 days after their last exposure. Vaccination is one of the methods to boost our antibodies. In Malaysia, there are 79.8% had been completed first dose and 78.7% completed second doses (*Vaccinations in Malaysia*, n.d.). When a large portion of a community (the herd) becomes immune to a disease, disease transmission from person to person becomes unlikely. As a result, the entire community, not just individuals who are immune, is protected (*Herd Immunity and COVID-19 (Coronavirus): What You Need to Know*, 2021).
**CONCLUSION AND RECOMMENDATIONS**
The spreading of COVID-19 is an interesting topic to discuss as it grows every day in Malaysia and the whole world. This study helps select effective ways to prevent COVID-19 from spreading using the Fuzzy Analytic Hierarchy Process (AHP) Method. In research from Sarwar and Imran (2021), COVID-19 has infected people in 215 countries throughout the world. It is estimated that more than 11 million people are afflicted worldwide. To stop the spread of coronavirus, the World Health Organization (WHO), Centers for Disease Control and Prevention (CDC), and other governing bodies issued rules. In this study, these suggestions and preventative measures were chosen.
The Analytical Hierarchy Process technique, along with a fuzzy approach, is employed in this study. Fuzzy AHP should be used to represent these linguistic variables because the decision-maker's preferences are based on both tangible and intangible criteria. Hence Fuzzy AHP method is utilized to select the effective ways to prevent COVID-19. The selection is based on seven criteria, which are social/physical, health monitor, unnecessary touching things, hygiene, immunity/fitness, healthy diet, and sharing personal items. Based on the result from this study, we can conclude that hygiene is the most important in selecting the effective ways to prevent COVID-19 from spreading which are wearing a mask, hand wash/sanitizer, and covering cough and sneezes. Moreover, social/physical and health monitor also important in preventing COVID-19 from spreading. The importance of each of the key prevention strategies (criteria) have been ranked.
In future studies to assess the spread of coronavirus, many more preventive measures, as well as different decision-making methodologies, may be studied. For example, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Elimination and Choice Expressing Reality (ELECTRE), Preference ranking organization method for enrichment evaluation (PROMETHEE), Decision making trial and evaluation laboratory (DEMATEL), Analytic network process (ANP), etc., can be other methods to be applied in this study.
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