key: cord-1012935-aq33yyyl
authors: Hezer, Seda; Gelmez, Emel; Özceylan, Eren
title: Comparative Analysis of TOPSIS, VIKOR and COPRAS Methods for the COVID-19 Regional Safety Assessment
date: 2021-03-24
journal: J Infect Public Health
DOI: 10.1016/j.jiph.2021.03.003
sha: e7f01491a2d5417ffdbb52a3c73317ab6e0e3f54
doc_id: 1012935
cord_uid: aq33yyyl

COVID-19, which emerged in December 2019, has affected the entire world. Therefore, COVID-19 has been a subject of research in various disciplines, especially in the field of health. One of these studies was the report made by the Deep Knowledge Group (DKG) consortium in which safe regions for COVID-19 were determined. In the report, the main criteria of quarantine efficiency, government efficiency of risk management, monitoring and detection, health readiness, regional resilience, and emergency preparedness are used in the evaluation of countries and regions (alternatives). As the data and research structure used in this report are based on multi-criteria, the purpose of this study is to evaluate and analyse the safety levels of 100 regions in the world in terms of COVID-19 using Technique for Order Performance by Similarity to Ideal Solution (TOPSIS), Vise Kriterijumsa Optimizacija I Kompromisno Resenje (VIKOR) and Complex Proportional Assessment (COPRAS) methods. The data and information required in the methods were obtained from a report prepared by the DKG. The results of the methods were compared with the ranking results presented in a report of the DKG. Accordingly, it has been observed that the method that provides the closest results to the results of the report is the COPRAS method, and the method that gives the most distant results is the VIKOR method.

Coronavirus, or "COVID-19", emerged on 1 December 2019 in Wuhan, the capital of the Hubei region in China. This virus started to spread rapidly to China and other parts of the world at the beginning of 2020 (Ozili, 2020) , and the number of infected patients has increased exponentially (Huang et al., 2020) . Because the virus is highly contagious , effective treatment is urgently needed (Metha et al., 2020) . The effects of the novel J o u r n a l P r e -p r o o f Risk Assessment" (DKG, 2020) . In the relevant research, 130 qualitative (exit strategy plan, state of emergency readiness, local vaccine development attempts, export-oriented region and other parameters) and quantitative (population density, number of cases, length of quarantine, literacy rate, number of hospital beds, number of doctors, and other parameters) parameters were used, and 200 regions were grouped into four different levels (Levels 1 to 4) according to the score value in terms of safe region. Level 1 consists of 20 regions with extremely high regional safety levels. Level 2 consists of 20 regions that do not have the same levels of security as the regions in Level 1 but score well in terms of regional safety. Level 3 consisted of 60 regions with fewer positive scores. The 100 regions with the least number of points constituted Level 4. The relevant levels and regions are listed in Table 1 .

The 130 parameters used in the pre-analysis were classified under six main criteria: quarantine efficiency, government efficiency of risk management, monitoring and detection, health readiness, regional resilience, and emergency preparedness. Quarantine efficiency includes elements such as quarantine scale, quarantine timeline, and travel restriction. The government efficiency of risk management includes elements such as economic sustainability, the efficiency of the government structure, and preparedness for a pandemic. Monitoring and detection consist of elements such as monitoring systems and disaster management, the scope of diagnostic methods, and test efficiency. Healthcare readiness consists of elements such as COVID-19 equipment availability, mobilisation of new healthcare services, and the quantity and quality of medical staff. Regional resilience consists of factors such as the risk of infection spread, cultural characteristics and social discipline, and chronic diseases.

Emergency preparedness consists of elements such as societal emergency resilience and J o u r n a l P r e -p r o o f emergency military mobilisation experience. The COVID-19 regional safety ranking hierarchy of the report is shown in Figure 1 .

As the report presents many criteria for decision-making, MCDM techniques can aid in making the rank list, considering the structure of the report and the determining criteria.

Therefore, in this study, rankings were made using the data from the report (DKG 2020) and MCDM techniques to determine the safe regions.

In this section, information about TOPSIS, VIKOR, and COPRAS methods are provided, which are MCDM techniques used in ranking the safe regions. Deterministic MCDM techniques are preferred because the data presented in the DKG report are deterministic.

When the problem includes uncertainty, popular fuzzy MCDM methods (Zadeh, 1965; Atanassov, 1986; Chen, 2000; Mendel et al., 2006; Chen and Lee, 2010; Özceylan and Paksoy, 2013; Ghorabaee et al., 2016; Gnanavelbabu and Arunagiri, 2018; Liu et al., 2020; Wang and Li, 2020) should be used to come with the imprecise data.

Among the various MCDM techniques, the TOPSIS method (Hwang and Yoon, 1981) has gained popularity because of its simple computational steps, solid mathematical foundations, and easy-to-understand method (Chakraborty, 2019) . This method ranks the alternatives according to the distance between the positive and negative ideal solutions (Wu et al., 2011) .

However, an alternative chosen while making a decision is expected to be close to the ideal J o u r n a l P r e -p r o o f solution and far from the non-ideal (negative ideal) solution (Lai et al., 1994) . The alternative that is closest to the positive ideal solution is also considered as the alternative that is the furthest from the negative ideal solution. The alternative closest to the positive ideal solution with the TOPSIS method is the best alternative (Cheng et al., 2002) . The TOPSIS method can be used to evaluate decision-making units (DMUs). If m indicates the number of alternatives and n indicates the number of evaluation criteria, indicates the value of the ℎ alternative according to the ℎ criterion. The TOPSIS method consists of the following steps (Wu et al., 2011) :

Step 1. Decision matrix ( = [ ] × ) is normalized.

= (ℎ ) × is defined as the normalised decision matrix, and the normalised criterion value ℎ is calculated using Eq. (1).

Step 2. The weighted normalized decision matrix is determined.

= ( ) × is defined as the normalised weighted decision matrix of = (ℎ ) × . When is the weight of the ith criterion, the normalised weighted value is calculated using Eq. (2).

= ℎ = 1,2, … . , ; = 1, 2, … . ,

Step 3. Positive-ideal and negative-ideal solutions are determined.

Positive-ideal and negative-ideal solutions were determined using Eq. (3) and Eq. (4), respectively. Ωb and Ωc represent the sets of benefit type and cost type criteria, respectively. * = { 1 * , … . . , * } = {(max | ∈ ) , (min | ∈ ) } (3)

Step 4. Euclidean distance is calculated from positive-and negative-ideal solutions.

The Euclidean distances of each alternative solution to the positive ideal ( * ) and negative ideal ( − ) solutions are calculated using Eq. (5) and Eq. (6). * = √∑( − * ) 2 =1 = 1, 2, … . ,

Step 5. Closeness to the ideal solution is calculated.

The closeness to the ideal solution formulated with can be defined as shown in Eq. (7).

Step 6. The order of all alternatives is determined based on their relative closeness to the ideal solution. A larger indicates a better alternative. The best alternative is the one with the largest closeness to the ideal solutions.

The TOPSIS method can be applied with different evaluation criteria and is frequently used in practice. At this point, when the literature is examined, it is seen that the TOPSIS method is used in many areas such as the automotive sector ( 

The VIKOR method was developed for the multi-criteria optimisation of complex systems.

It determines the compromise order list, the compromise solution, and the weight stability ranges for the preferred stability in the obtained compromise solution with the initial (given) J o u r n a l P r e -p r o o f weights. This method focuses on ordering and selecting a range of alternatives in the presence of conflicting criteria. It offers a multi-criteria ranking index based on the measure of "closeness" to the "ideal" solution (Opricovic and Tzeng, 2004) . This method is an effective tool used in MCDM, especially when the decision-maker cannot express their preferences at the beginning of the system design (Opricovic and Tzeng, 2007) . At the same time, this method focuses on ordering and choosing from a range of alternatives. It determines a compromise solution for problems with conflicting criteria that can help decision-makers reach a final solution (Sayadi et al., 2009) . The development of the VIKOR method starts with the − criterion form given by Eq. (8) (Opricovic and Tzeng, 2004 )

In the VIKOR method, , (Sj in Eq. (11)) and ∞, ( in Eq. (12)) ordering measurements were used by formulating. The aim is to obtain with maximum group utility ("majority" rule) and with minimal individual regret of the "opponent." The compromise solution is the result closest to the ideal * . Compromise means an agreement with mutual concessions by ∆ 1 = 1 * − 1 and ∆ 2 = 2 * − 2 as shown in Figure 2 . The compromise ordering steps of VIKOR are as follows (Opricovic and Tzeng, 2004) :

Step 1. The best ( * ) and worst ( − ) values of all the criteria functions were determined.

where i= 1, 2, .., n, and the i th function represents a benefit. * and − are calculated using Eq. (9) and Eq. (10), respectively, as follows: * = max

J o u r n a l P r e -p r o o f − = min (10)

Step 2. and values are calculated using Eq. (11) and Eq. (12), respectively ( = 1, 2, . . . , ).

where is the criterion weight, whose relative significance is expressed.

Step 3. The value is calculated using Eq. (13), Eq. (14), and Eq. (15) (j=1, 2, . . . , m): * = min , − = max (13) * = min , − = max (14)

where x represents the strategic weight of the majority of criteria (or maximum group utility).

In this study, x = 0.5.

Step 4. Three ordering lists are created by arranging the S, R, and Q values of the alternatives in ascending order.

Step 5. If the two conditions stated below are met, alternative (a′), which ranks according to the best Q (minimum) values, is recommended as a compromise solution.

′′ is the second alternative in the ranking list. Eq. (16) and Eq. (17) need to be satisfied to fulfil Condition 1.

where m is the number of alternatives.

J o u r n a l P r e -p r o o f 10 Alternative ′ is the best alternative and must also be ranked according to the S and/or R values. This compromise solution is stable during the decision-making process. v is the weight of the decision-making strategy. If one of these conditions is not satisfied, a compromise set of solutions is suggested. This set of solutions includes the following:

• Alternative ′ and ′′ only if Condition 2 is not met.

• Alternatives ′ , ′′ , … . . , ( ) if Condition 1 is not satisfied and ( ) is determined for the maximum with ( ( ) ) − ( ′ ) < relation (closeness to the positions of these alternatives).

The best alternative, ranked according to Q values, is the alternative with a minimum Q value.

The main ranking result is a compromise solution with a compromise ranking list of alternatives and an "advantage ratio".

VIKOR is effective in a situation when the decision-maker is not aware of the design of the system. The compromise solution obtained is accepted by the decision-maker for the maximum group benefit of the majority (denoted by Eq. (11)) and the minimisation of the individual regrets of the opponents (denoted by Eq. (12)).

According to the literature, the VIKOR method is used in decision-making analyses in many studies in different disciplines, such as the automotive sector (Luthra et al., 2017) 

The "Complex Proportional Assessment" or COPRAS method was introduced by Zavadskas and Kaklauskas (1996) and was used to evaluate the superiority of one alternative J o u r n a l P r e -p r o o f 11 over another and makes it possible to compare alternatives (Zavadskas et al. 2009 ). This method can be applied to maximise or minimise criteria in an assessment where more than one criterion should be considered (Podvezko 2011) . The COPRAS method ranks and evaluates alternatives step-by-step for their importance and utility degree (Kaklauskas et al., 2010) . The steps of the COPRAS method are as follows (Chatterjee et al., 2011):

Step

The normalised decision matrix is denoted by = [ ] × . The purpose of normalisation is to obtain different dimensionless values to compare all criteria.

Step 2. The weighted normalised decision matrix = [ ] × was determined using Eq.

(19).

Where is the normalized value of ℎ alternative according to ℎ criterion.

Step 3. The sums of the weighted normalised values were calculated for both the beneficial and non-beneficial criteria. These sums were calculated using Eq. (20) and Eq. (21).

where + and − are the weighted normalised values of the beneficial and nonbeneficial criteria, respectively. The larger the + value and the lower the − value, the better the alternative. The values of + and − indicate the degree of goals reached by each alternative.

J o u r n a l P r e -p r o o f 12

Step 4. The significance of the alternatives is determined by defining the characteristics of the positive alternatives + and negative alternatives − .

Step 5. The relative significance or priorities of the alternatives were determined. The priorities of the candidate alternatives were calculated based on . The higher the value, the higher is the priority of the alternative. The relative significance of an alternative shows the degree to which it fulfils the demand provided by that alternative. The alternative with the highest relative significance value (C_max) is the best choice among the candidate alternatives. The relative significance value of the ℎ alternative, , was calculated using Eq.

(22).

where − is the minimum value of − .

Step 6. The quantitative utility ( ) was calculated for the ℎ alternative. The utility level of an alternative is causally related to its relative significance value ( ). The degree of utility of an alternative, determining the rank of the alternative, is determined by comparing the priorities of all alternatives for efficiency. It is calculated using Eq. (23).

where Cmax is the maximum relative significance value. As the relative significance value increases or decreases for an alternative, its utility value also increases or decreases. The MCDM techniques can be used to solve problems related to the COVID-19 pandemic in health (Majumder et al., 2020; Sayan et al., 2020; Albahri et al., 2020; Shirazi et al., 2020) , education (Alqahtan and Rajkhan, 2020), and various fields (Vinodhini, 2020; Korzeb and Niedziółka, 2020) . The purpose and the methods used for some of these studies are summarized and presented in the subsequent paragraphs.

Albahri et al. (2020) present a systematic approach to evaluate and compare various artificial intelligence techniques used to detect and classify medical images of the novel coronavirus. VIKOR methods were used for the process. Further, the analytic hierarchy process (AHP) was used in weighting.

In the study by Vinodhini (2020) Alqahtani and Rajkhan (2020) 

This section consists of three subsections. In the first sub-section, brief information is provided regarding the alternatives considered. In the second subsection, information regarding the criteria and weights used in this study is presented in detail. In the concluding section, the results are presented. 

The evaluation criteria used for the study were based on the six categories mentioned in the DKG report (2020). The values of each alternative for Level 1, Level 2, and Level 3 are presented in Table A1 , Table 2, and Table A3 , respectively, and the details are given in the Appendix.

Two different prioritizations are considered in this study. In the first prioritisation, the criterion weights suggested by the DKG are normalised, and in the second prioritisation, analyses are carried out with the assumption that all criteria weights are equal. In the applied methods, the criteria should be specified according to their orientation for benefit or cost. The criterion with the smallest (least cost) value in cost-oriented criteria and the criterion with the highest (the most benefit) value in benefit-oriented criteria should be determined as the best criterion. The six criteria used in this study are benefit-oriented in achieving the objective of the study (ensuring regional safety in terms of COVID-19). In other words, the high values of these criteria aid in determining the best alternative. The criteria used in this study and their weights are listed in Table 2 .

[ Normalised results obtained by applying equal weights are presented for the TOPSIS method in the third, fourth, and fifth columns, for the VIKOR method in the next four columns, and the COPRAS method in the last four columns. In the rows, the alternatives included in Level 1 are given in Table 3 , Level 2 is given in Table 4 , and Level 3 is given in Table 5 .

According to Table 3 ,  As in the DKG report, Switzerland ranked first in all methods and prioritisation. Arabia, and Hungary) is the same as the DKG report ranking in at least three methods.

According to Table 4 ,  Kuwait, which ranks first in the report, maintains its place in all the methods.

 The ranking of the three regions for normalised weights (Kuwait, Qatar, Greece) and the two regions for equal weights (Kuwait, Finland, Greece, Estonia, and Cyprus) using the TOPSIS method, the ranking of four regions for normalised weights (Kuwait, Iceland, Qatar, Liechtenstein) and two regions for equal weights (Kuwait, Liechtenstein) using the VIKOR method, and the ranking of eight regions for normalised weights (Kuwait, Iceland, Bahrain, Finland, Liechtenstein, Greece, Estonia, Croatia) and nine regions for equal weights (Kuwait, Finland, Luxembourg, Qatar, Lithuania, Malaysia, Greece, Estonia, Ireland) using the COPRAS method are the same as the ranking in the report.

 The ranking of six regions (Kuwait, Finland, Qatar, Liechtenstein, Greece, and Estonia) is the same as the ranking in at least three methods.

[  While Chile takes first place in the report, France takes first place in six applications.

It can be seen that the success of the compromise solutions with reports provided by all three methods decreased from Level 1 to Level 3. When the methods are evaluated individually, it is observed that the ranking results are not exactly the same. Tables 3, 4 , and 5, it is found that for some regions, the ranking remains the same for the same method irrespective of the weight change. However, the ranking of many regions varies within the same method with weight change. For example, in the TOPSIS method, Switzerland, Germany, and Israel maintain their rankings,

while Singapore ranks seventh in the results obtained by applying normalised weights and eighth in the results obtained by applying equal weights, respectively, as shown in Figure 3 and Table 3 .

The evaluation of the results reveals that Switzerland ranks first for all methods and prioritisation. Similarly, Kuwait, which ranks first in the report in Level 2, maintains its ranking position in all methods and prioritizations. For Levels 1 and 2, it is determined that similarities and differences occur in rankings according to normalised and equal weights. In Level 3, while Chile ranked first in the report, France ranked first in six applications.

In this study, 100 regions of the world were analysed using TOPSIS, VIKOR, and COPRAS methods to determine their regional safety levels for COVID-19. The data used within the scope of the analysis were taken from the report (DKG, 2020) presented by the DKG, and evaluation was made by comparing the results obtained in this study with the report.

The regions Level 1, Level 2, and Level 3 constitute the alternatives. Unlike the DKG report used to obtain the data, Level 4 is not considered because the data required by the methods are insufficient. The six criteria used in this study were evaluated as benefit-oriented with the purpose of the study, which was determined to ensure regional safety in terms of COVID-19. Each region (Level 1, Level 2, and Level 3) is analysed comparatively with TOPSIS, VIKOR, and COPRAS methods, and the results are presented.

It was concluded that the COPRAS method obtained the most compatible results with the DKG report. The TOPSIS method gives a compromised result related to the report. It is observed that the VIKOR method provide the least compatible result. It has been observed that regions with an above-average score generally according to the government efficiency of risk management and quarantine efficiency criteria, which have the highest weight value, ranked high in the rankings.

Considering that MCDM techniques are auxiliary instruments for decision-makers, they are more appropriate to evaluate all methods than to suggest a single method. Decisionmakers primarily evaluate the results of COPRAS. However, they should also consider the results of TOPSIS and VIKOR. In future studies, MCDM techniques that are different from the ones used in this study could be considered. By examining the procedures followed by the regions in their struggle against COVID-19 and their status, new criteria or sub-criteria presented in the DKG report (DKG, 2020) can be added to the criteria presented in this study, or MCDM methods can be applied by removing some criteria from the existing criteria.

Further, fuzzy data that reflect the uncertainty of the real-life situation can be utilised.

Therefore, fuzzy MCDM techniques can be used to solve the problem. 

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 Finland  47  63  62  74  65  45   Georgia  52  55  61  61  50  45   Greece  48  63  57  61  65  43   Iceland  53  63  69  68  67  44   Ireland  46  60  57  59  65