During the COVID-19 pandemic, masks have become essential items for all people to protect themselves from the virus. Because of considering multiple factors when selecting an antivirus mask, the decision-making process has become more complicated. This paper proposes an integrated approach that uses F-BWM-RAFSI methods for antivirus mask selection process with respect to the COVID-19 pandemic. Finally, sensitivity analysis was demonstrated by evaluating the effects of changing the weight coefficients of the criterion on the ranking results, simulating changes in Heronian operator parameters, and comparing the obtained solution to other MCDM approaches to ensure its robustness.
The COVID-19 pandemic, which is the result of the SARS-CoV-2 virus, has spread around the world in a short time since its emergence in Wuhan, China, mobilized international health authorities and its effect continues to be serious. The studies and reports published by the World Health Organization on the pandemic are followed with interest and concern by the whole world.
Studies examining the effects of the virus on China’s and the world’s economy have revealed that the virus caused a loss of approximately 62 billion dollars to the Chinese economy and more than 280 billion dollars to the world economy in the first quarter (Ayittey
In line with the instructions of the World Health Organization (WHO) against this pandemic that threatens international public health, national administrations also take various measures to protect public health and to get rid of the epidemic with the least damage. However, despite the strictness of the measures, the continuous increase in death cases due to the impact of the epidemic and the epidemic itself causes serious concerns at the international level.
When the reports and scientific studies published by the WHO were examined, it was determined that the demand for healthcare materials such as protective masks and gloves has increased worldwide since the outbreak occurred and that the prices of related healthcare materials also increased significantly due to the increase in demand (Mahase,
Fuzzy multi criteria decision-making (MCDM) methods are commonly used for decision-making in medical and healthcare fields (Kumar
It can be clearly seen that the integrated MCDM methods based on fuzzy set theory are widely used in the fields of medical and healthcare. However, there are limited studies about the selection of personal protective equipment, especially antivirus masks, during the COVID-19 pandemic.
This paper proposes an integrated approach that uses fuzzy BWM and Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval (F-BWM-RAFSI) methods for antivirus mask selection process with respect to the COVID-19 pandemic. Due to the vagueness of data and the ambiguity of decision-maker, the involvement of the fuzzy concept into MCDM can obtain much more reliable results in real-life applications. The F-BWM approach which combines the fuzzy set theory and BWM can provide more consistent comparisons. It has been demonstrated that the BWM method performs significantly better than other MCDM methods such as AHP in terms of consistency index, minimum violation, total deviation and conformity (Rezaei,
The rest of the paper is presented as follows: Section
The primary transmission route of COVID-19 is respiratory droplets and contact. During the COVID-19 pandemic, personal protective equipment like antivirus masks has become essential items for medical staff and people to work and travel. Therefore, selection of the personal protective equipment such as antivirus masks are especially important. This paper focuses on the selection process of the antivirus masks under the COVID-19 pandemic situation and aims to address the following research questions (RQs):
Which criterion is more important for selecting an antivirus mask?
How to effectively evaluate the antivirus masks through the subjective judgment of group experts in medicine sector?
How to build a decision-making approach that evaluates the antivirus mask alternatives?
To answer these RQ’s, this study proposes a new hybrid MCDM method that will be addressed here for the first time in order to be applied to a medical mask selection problem. One of the novel MCDM methods, called RAFSI method under a fuzzy environment, can be easily used for solving complex problems. The novelties found in the methodological application of this study are as follows: 1) A new extension of the BWM and RAFSI MCDM model using fuzzy sets is introduced in this paper. The model provides a more objective experts’ evaluation of the criteria and alternatives in a subjective environment. The present methodology enables the evaluation of alternative solutions despite dilemmas in the decision-making process and a lack of quantitative information. 2) Using fuzzy sets in the RAFSI methodology instead of using a crisp value, the structure of the given data is exclusively used. In this way, the uncertainties present in the data are used, thus improving the objectivity of the decision process. According to the authors, the application of fuzzy numbers for the purpose of exploiting the uncertainty that occurs during criteria and alternatives group evaluation using the BWM-RAFSI method has not been considered in the literature so far. Fuzzy numbers allow for the transformation of the uncertainties and inaccuracies present during the evaluation of alternatives and criteria pairwise comparisons.
In sum, the contributions of this paper can be highlighted as follows:
It presents a framework that helps the selection of personal protective equipment such as antivirus masks during COVID-19 pandemic. It performs a comprehensive evaluation of the antivirus mask selection process through a new MCDM method F-BWM-RAFSI. Although the RAFSI technique is a powerful decision-making tool, it cannot express fuzziness and ambiguity information. Combined with the fuzzy sets, we posit the fuzzy RAFSI model, which can better describe decision-makers’ evaluation information. We extend assessments of decision-makers to the fuzzy sets to extract criteria weights and rank the alternatives. F-BWM-RAFSI approach is suggested to apply to multiple criteria group decision making (MCGDM) problems. It presents a real case study with respect to the evaluation of the antivirus mask alternatives; and It performs a sensitivity analysis to validate the proposed quantitative evaluation process.
This study proposes a new hybrid MCDM method that will be addressed here for the first time in order to be applied to a medical mask selection problem. Rezaei (
Systematic steps of the integrated methodology.
The fuzzy set theory was introduced by Zadeh in 1965 for better reflecting on human judgments and assessment in the decision-making process. Real case decision-making problems include fuzziness and uncertainty, as decision, goals, constraints, decision-maker opinions are not completely known. For that reason, group decision maker problems practically have used fuzzy numbers (Zadeh, Let
Triangular fuzzy numbers.
Some triangular fuzzy operations (Carlsson and Fullér, Also, the mathematical operations of the triangular fuzzy number are formulated in Table Assume
Fuzzy BWM method have been applied successfully in various areas such as evaluating the sustainable supplier selection criteria (Ecer and Pamucar,
In addition, BWM has been incorporated with a different type of fuzzy sets such as interval type-2 fuzzy number (Wu
The fuzzy pairwise comparisons are applied based on the linguistic terms given in Table
Considering
The GMIR formula is as follows:
Consistency index values for F-BWM (Guo and Zhao,
Linguistic terms | Equally important (EI) | Weakly important (WI) | Fairly important (EI) | Very important (VI) | Absolutely important (AI) |
3 | 3.8 | 5.29 | 6.69 | 8.04 |
Ranking of Alternatives through Functional mapping of criterion subintervals Into a Single Interval (RAFSI) method (Žižović
Since we have a group decision-making model, we obtain
Thus, we obtain a standardized decision matrix
COVID-19 is an infectious disease that primarily spreads out between humans through direct contact with an infected person or their respiratory droplets. Respiratory droplets are generated by breathing, speaking, coughing, and sneezing. Droplet nuclei are respiratory droplets that dry quickly after expiration and shrink to a diameter of less than 5 m. Droplet nuclei remain suspended in air and can travel over long distances. Goggles and respiratory protection are recommended for airborne prevention; a medical mask is needed to avoid COVID-19 infection from spreading via the air (Azap and Erdi˙nç,
This study presents integrated methods that use fuzzy BWM and RAFSI-F approach-based framework for mask selection with respect to COVID-19 disease. We have five experts who are caring for coronavirus patients in the hospital in Istanbul and Bursa which are two cities with the highest population density in Turkey. The details of experts are indicated in Table
Expert information.
Experts | Profession | Experience | Department | Location |
EX1 | Doctor | 5 years | Public Health | Istanbul |
EX2 | Doctor | 3 years | Internal Medical | Istanbul |
EX3 | Doctor | More than 10 years | Infectious diseases and clinical microbiology | Istanbul |
EX4 | Doctor | More than 15 years | Infectious diseases and clinical microbiology | Bursa |
EX5 | Doctor | More than 15 years | Infectious diseases and clinical microbiology | Bursa |
The F-BWM was applied to determine the relative weight scores of the antivirus mask selection criteria and then, the most favoured mask is selected by the RAFSI-F approach using the evaluated weights. For this purpose, the criteria determined in the selection of medical masks and short description were obtained from expert opinions and literature review, mask selection criteria are identified in Table
Mask selection criteria.
Code | Criteria | Brief description |
C1 | Leak age rate (fitting rate for face) | Covers the face perfectly, does not stretch or sag |
C2 | Quality of raw material | Manufactured using non-woven fabric material, its pores should be small and it should be made in accordance with health procedure |
C3 | Reusability | Has two or more layer washable |
C4 | Breathability | Allows comfortable breathing |
C5 | Use of hypo-allergenic materials | Contains non-harmful particles and carcinogen substance |
C6 | Easy to wear and take off | Conformity to the face |
C7 | Filtration rate | Preserves the respiratory system against the viruses |
C8 | Tear and deformation resistant | Has a durable and undeformed material |
Six different types of medical masks including basic cloth face mask, surgical face mask, single use face mask, particulate respirators (N95 and above), full face respirator and full-length face shield and their descriptions are also shown in Table
Medical mask alternatives.
Code | Figure | Name | Statement |
Basic cloth mask | This is a typical face mask recommended for public to avoid spreading coronavirus, everyday version of a face mask. | ||
Surgical face mask | A variation of this face mask is worn by medical professionals who are presently doing COVID-19 drive-thru testing. It’s a mask that doctors and nurses use. The safety factor is pretty high, and it has good antibacterial and antiviral resistance. | ||
Single use face mask | This is a disposable mask that prevent leaks from nose and mouth. However, it not intended for medical use. It is made of a single-use plastic product. | ||
Particulate respirators (N95 and above) | This kind of face mask is essential for medical staff and first responders. When the user inhales, it filters out both large and micro particulates, providing better protection than a medical mask. | ||
Full face respirator | A full-face respirator is a type of mask that is commonly used in home basic repairs and be a good choice for providing coronavirus assistance. However, it can cause some breathing problems or respiratory issues. | ||
Full-length face shield | This is a flimsier, plastic variant of the glass masks used on welders. It has a padded headband that covers the full face from brow to chin. |
Best criteria and Best to Other (BO) vectors identified by experts.
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | ||
EX 1 | C7 | WI | AI | FI | VI | AI | AI | EI | VI |
EX 2 | C7 | WI | FI | VI | WI | WI | AI | EI | VI |
EX 3 | C7 | EI | VI | FI | FI | VI | FI | EI | FI |
EX 4 | C7 | WI | WI | WI | WI | FI | AI | EI | WI |
EX 5 | C7 | FI | FI | AI | VI | VI | FI | EI | VI |
Worst criteria and Other to Worst (OW) vectors identified by experts.
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | ||
EX 1 | C6 | FI | WI | FI | WI | WI | EI | AI | WI |
EX 2 | C6 | VI | FI | WI | VI | WI | EI | AI | WI |
EX 3 | C5 | AI | FI | FI | VI | EI | FI | VI | FI |
EX 4 | C6 | FI | FI | FI | FI | WI | EI | AI | FI |
EX 5 | C3 | WI | WI | EI | FI | WI | WI | AI | WI |
Solving above model by using LINGO 18.0 software, the optimal fuzzy weights with regards to EX1 can be calculated, which are:
Then, all F-BWM steps have been implemented for each expert. Results of all optimal fuzzy weights and average optimal fuzzy weights (AOFW) of eight criteria are given in Table
Optimal fuzzy weights for five experts.
EX1 | EX2 | EX3 | EX4 | EX5 | AOFW | |
According to the results of the F-BWM model, among the antivirus mask criteria, “Filtration rate (
Average crisp weight for each criterion.
Consistency ratio.
CI | CR | ||
EX1 | 0.4494 | 8.040 | 0.055 |
EX2 | 0.7912 | 8.040 | 0.098 |
EX3 | 0.6093 | 6.690 | 0.091 |
EX4 | 0.6232 | 8.040 | 0.077 |
EX5 | 0.5000 | 8.040 | 0.062 |
After defining the weight coefficients of the criteria, five experts evaluated the alternatives
Fuzzy linguistic scale.
Linguistic terms | Membership function |
Very Poor (VP) | (1, 1, 1) |
Poor (P) | (1, 2, 3) |
Medium Poor (MP) | (2, 3, 4) |
Medium (M) | (3, 4, 5) |
Medium High (MH) | (4, 5, 6) |
High (H) | (5, 6, 7) |
Very High (VH) | (6, 7, 8) |
Extremely High (EH) | (7, 8, 9) |
Absolutely High (AH) | (8, 9, 9) |
After evaluating the alternatives, the experts’ correspondence matrices were obtained and are shown in Table
The experts’ correspondence matrices.
Criteria | |||
VP; P; M; P; MH | VP; P; MP; MH; M | VP; P; M; H; M | |
MH; MH; MP; MP; P | H; M; M; MH; VH | MP; MP; MP; MP; VH | |
H; MH; VP; AH; EH | VP; VP; VP; VP; VP | VP; VP; VP; VP; VP | |
H; MH; VH; MH; EH | M; M; VH; MP; VH | MH; MH; VH; MP; VH | |
M; MH; MH; M; M | VH; M; EH; VH; EH | MH; M; EH; MP; EH | |
EH; VH; EH; EH; VH | VH; M; EH; EH; AH | H; M; MH; VH; AH | |
MP; MP; P; P; MP | EH; M; MP; MH; VH | VP; P; P; MH; VH | |
H; M; P; H; EH | MP; MP; P; MP; MH | MP; MP; VP; MP; MH |
Criteria | |||
VP; VP; VP; P; P | VP; P; VP; P; P | VP; MP; P; VH; MH | |
MH; M; EH; EH; EH | H; MH; EH; AH; EH | VP; VP; H; MP; EH | |
M; M; M; MH; VP | EH; VH; EH; AH; VH | VP; M; VH; MP; VH | |
M; M; H; MP; M | P; VP; MH; P; MH | VP; M; H; M; AH | |
MH; MH; EH; VH; EH | MH; P; H; VH; EH | VP; VP; H; H; EH | |
MP; M; H; P; VH | MP; VP; MP; P; VH | VP; MH; M; MP; AH | |
EH; H; VH; EH; AH | EH; EH; VH; EH; EH | VP; VP; M; P; VH | |
MH; M; H; MH; VH | EH; H; EH; EH; EH | VP; P; H; MP; VP |
By applying expression (
The aggregated initial decision matrix.
Criteria | ||||||
The element at position
The standardized initial decision matrix.
Criteria | ||||||
By substituting the values from the aggregated initial decision matrix into the function
Normalized initial decision matrix.
Criteria | ||||||
The ranking of alternatives.
Alt. | Fuzzy value ( |
Crisp value ( |
Rank |
0.3930 | 4 | ||
0.4255 | 3 | ||
0.3569 | 6 | ||
0.5477 | 2 | ||
0.5726 | 1 | ||
0.3611 | 5 |
Based on the obtained results, we can single out the antivirus mask A5 as the dominant solution, i.e. the following ranking of alternatives is proposed:
To verify the proposed solution, the sensitivity analysis of the fuzzy BWM-RAFSI model is presented in the following section. After obtaining the initial results in the MCDM framework, the question arises as to how subjectively defined input parameters influence decision making and what solutions are obtained by applying other multi-criteria techniques (Muhammad
It is indisputable that the results of multi-criteria models largely depend on the values of the weight coefficients of the criteria. In this study, experts’ preferences were used to determine the weight coefficients of the criteria, which were processed using fuzzy BWM. Since this is a subjective model for determining the weights of the criteria, the question arises as to how these subjective assessments affect the final results of the research. Since the greatest influence on the final decision has the criterion that has the highest value of the criteria weight
Influence of change of criteria weights on change of criterion functions of alternatives
The analysis shown in Fig.
By changing the values of the parameters
Influence of parameters
The presented experiments showed that changes in the values of the parameters
Since the Heronian function was used to aggregate values from experts’ initial decision matrices into an aggregated initial decision matrix, this section analyses the impact of changing the
Influence of parameters
The values of the criterion functions of the alternatives (Fig.
Since fuzzy sets were used for uncertainty processing in this paper, four fuzzy multicriteria techniques were chosen to compare the results: fuzzy COPRAS (Complex Proportional Assessment) technique (Fouladgar
A comparative overview of the application of these fuzzy MCMD methodologies is shown in Fig.
Ranks of the alternatives based on the different fuzzy methodology.
Based on the obtained results, it was confirmed that alternative
COVID-19 has spread more like most other common respiratory diseases, mainly through respiratory droplet transmission without physical contact. Therefore, wearing a face mask is one of the most effective ways to prevent the spread of the virus. Especially, health workers are the most likely to be exposed to COVID-19 because they are in close contact with patients with suspected, probable or confirmed COVID-19. During the COVID-19 epidemic, face masks have become a highly effective item for health care staff and ordinary people. Different types of masks have been suggested throughout the COVID-19 pandemic. However, some masks are more effective than others. In order to determine what types of face mask work best to prevent the spread of COVID-19, this paper proposes a combined approach that uses F-BWM and fuzzy RAFSI methods for the mask selection process for healthcare personnel with respect to the COVID-19 pandemic to fill the gap in the literature.
There are two main advantages of the proposed fuzzy BWM-RAFSI methodology: 1) fuzzy BWM-RAFSI method has a new mathematical treatment for data normalization that enables transferring data from the initial decision making matrix into any interval which is adequate for making rational decisions and 2) resistance of fuzzy BWM-RAFSI method to rank reversal problem (Žižović
One of the possible limitations of the fuzzy BWM-RAFSI multi-criteria methodology is the mathematical complexity that requires the knowledge of nonlinear mathematical programming and fuzzy theory. This feature may be a limiting factor for a broader application in the multi-criteria decision-making field. To overcome this limitation, it is recommended that future research be directed towards developing a decision support system based on the application of the fuzzy BWM-RAFSI methodology. Also, a major source of limitation is that due to the over-intensity and high workload during the pandemic process, the opinions of healthcare workers such as nurses, medical technicians, dentists and etc. were not considered in this evaluation process.
Further research can benefit from the perspectives of healthcare workers from other professions and occupations. Furthermore, this proposed model can be performed for the same problem under newly released fuzzy extensions such as Pythagorean fuzzy sets, cubic picture fuzzy sets and spherical fuzzy sets for the future work. By doing this way, the validity of this hybrid model can be tested with the results obtained from several fuzzy sets. Finally, this new integrated model may be used in a variety of healthcare domains, including the development of an optimum COVID-19 diagnostic system, wearable health devices, and treatment techniques.