EvaluationoftheCOVID-19PandemicIntervention...

Research ArticleEvaluation of the COVID-19 Pandemic InterventionStrategies with Hesitant F-AHP

Funda Samanlioglu and Burak Erkan Kaya

Department of Industrial Engineering Kadir Has University Cibali 34083 Istanbul Turkey

Correspondence should be addressed to Funda Samanlioglu fsamanlioglukhasedutr

Received 18 May 2020 Revised 28 July 2020 Accepted 4 August 2020 Published 20 August 2020

Academic Editor Pasi A Karjalainen

Copyright copy 2020 Funda Samanlioglu and Burak Erkan Kaya is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

In this study a hesitant fuzzy AHP method is presented to help decision makers (DMs) especially policymakers governors andphysicians evaluate the importance of intervention strategy alternatives applied by various countries for the COVID-19pandemic In this research a hesitant fuzzy multicriteria decision making (MCDM) method hesitant fuzzy Analytic HierarchyProcess (hesitant F-AHP) is implemented to make pairwise comparison of COVID-19 country-level intervention strategiesapplied by various countries and determine relative importance scores An illustrative study is presented where fifteen inter-vention strategies applied by various countries in the world during the COVID-19 pandemic are evaluated by seven physicians (aprofessor of infectious diseases and clinical microbiology an infectious disease physician a clinical microbiology physician twointernal medicine physicians an anesthesiology and reanimation physician and a family physician) in Turkey who act as DMs inthe process

1 Introduction

As was realized from the previous 2009 AH1N1 pandemicand the recent COVID-19 pandemic countries need effi-cient mitigation planning to prevent mass infection andfatalities An effective intervention plan may help flatten theepidemic curve and with protective measures there mightbe a delay and reduction in the peak of the outbreak As aresult the number of cases at any time stays under the surgecapacity of a countryrsquos healthcare system If the surge ca-pacity of a countryrsquos healthcare system is exceeded themorbidity and mortality rates increase for all hospitalizedpatients not just for COVID-19 cases

e basic reproduction number (R0) is the key factor thatshows the strength of the epidemic it is without any in-terventions the mean number of secondary cases generatedby a single infected case in a population with no immunity toinfection [1] When R0 is greater than 1 the epidemic takeshold and the overall fraction of population likely to beinfected without interventions is the area under the epidemiccurve which can be calculated roughly with 1-1R0 [2]

Effective intervention strategies if followed properly mightreduce the R0 below 1 and control the spread of COVID-19

Countries need a systematic approach to determinewhich intervention strategies to apply during the COVID-19pandemic and future potential epidemiological waves andpandemics In this study intervention strategies applied bycountries during the COVID-19 pandemic are evaluated interms of importance with the help of an MCDM methodhesitant F-AHP Scenarios for the potential spread andimpact of COVID-19 in the EUEEA with suggested actionsfor containment were given in Johnson et alrsquos article [3]Also Cheng et al [4] presented an extensive dataset ofgovernment responses to the COVID-19 pandemic and theinterventions that are evaluated in this study are taken fromtheir research A list of these interventions is presented inTable 1 with detailed explanations and country examples

In the literature there is a limited number of studies thatfocus on the evaluation of intervention strategies Aledortet al [5] evaluated the evidence base for nonpharmaceuticalpublic health interventions in an influenza pandemic withthe help of literature review and expert opinions Ciofi degli

HindawiJournal of Healthcare EngineeringVolume 2020 Article ID 8835258 11 pageshttpsdoiorg10115520208835258

Table 1 COVID-19 intervention strategies and country examples

A1 Quarantinelockdown of patients and those suspected ofinfection

Policies to quarantine or shelter in place for at least 14 days For exampleldquoHong Kong a semiautonomous Chinese region requires travelers fromall countries to self-quarantine for 14 daysrdquo

A2 Internal border restrictions reducing the ability to movefreely (transportation) within a country

Government policies which reduce the ability to move freely within acountry For example in Peru as of March 15 2020 ldquoofficials are alsorestricting the movement of people across provincesrdquo

A3 Social distancingGovernment policies that limit physical contact between individuals to15 meters or 6 feet For example in Germany ldquoa 15 meter (49 feet)distance should be kept at all times when in publicrdquo

A4 Health monitoring

Government policies that seek to monitor the health of individuals whoare afflicted with or who are likely to be afflicted with the coronavirus Forexample ldquoTaiwan CDC monitors all individuals who had traveled toWuhan within 14 days and exhibited a fever or symptoms of upperrespiratory tract infectionsrdquo

A5 Public awareness campaigns

Efforts to disseminate and convey reliable information about COVID-19including ways to prevent or mitigate the health effects of COVID-19 Forexample on March 22 2020 it was announced that ldquothe ProvincialYouth Council in Namibia carried out an intense public awarenesscampaign on methods of disease prevention during which youngassociates distributed pamphlets with statements about the pandemicand ways of preventionrdquo

A6 Restriction of nonessential businesses

Government policies that restrict nonessential commercial activity Forexample in Serbia ldquoas of March 21 2020 the following measures are ineffect supermarkets gas stations restaurants post offices banks andother service providers will be reducing their hours to observe the curfewwith some closing at 6 00 PM or earlier Cafes restaurants and shoppingcenters are closed however food delivery is allowedrdquo

A7 Restrictions of mass gatherings

Government policies that limit the number of people allowed tocongregate in a place For example on March 16 2020 in the UnitedStates ldquothe latest recommendation announced Monday by the federalgovernment to promote social distancing and limit the transmission ofthe coronavirus is no more than 10 people in one placerdquo

A8 External border restrictions reducing the ability to exit orenter a country

Government policies which reduce the ability to access ports of entry toor exit from a country For example ldquoNamibian government suspendsinbound and outbound flights for 30 daysrdquo

A9 Closure of schoolsGovernment policy that closes educational establishments in a countryFor example in Slovakia as of March 12 2020 ldquoall schools andeducational establishments will be shut downrdquo

A10 Government policies that affect the countryrsquos healthresources (materials and health worker)

Government policies which affect the material (eg medical equipmentnumber of hospitals for public health) or human (eg doctors nurses)health resources of a country For example ldquoTaiwan bans exports of facemasks ban extended to the end of April (2020)rdquo or ldquoGovernmentapproves plan to build 60 production lines to make an additional 6million masks per dayrdquo

A11Formation of new task unitsbureaus and governmentpolicies changing administrative capacity to respondto the crisis

Government policy that changes the administrative capacity of a part ofgovernment to respond to the crisis For example on January 20 2020ldquoTaiwan activated the Central Epidemic Command Center (CECC)which mobilizes government funds and military personnel to facilitateface mask productionrdquo

A12 Common health testing (independent of suspectedinfection)

Government policies which seek to sample large populations forcoronavirus regardless of suspected likelihood of affliction withcoronavirus

A13 Curfew

Government policies that limit domestic freedom ofmovement to certaintimes of the day For example in Serbia ldquoas of March 21 2020 thefollowing measures are in effect curfew for all residents with fewexceptions from 800pm to 500am the next dayrdquo

A14 Restriction of nonessential government services

Government policy that restricts nonessential government services Forexample in Malaysia from March 18 2020 to March 31 2020 ldquoallgovernment and private services except those involved in essentialservices such as water electricity power telecommunications postaltransportation fuel finance banking health pharmacy fire portairport security retail and food supply will also be closedrdquo

A15 Declaration of emergencye head of government declares a state of national emergency Forexample on March 15 2020 in South Africa ldquoPresident Ramaphosaannounces national state of disasterrdquo

2 Journal of Healthcare Engineering

Atti et al [6] evaluated the diffusion of pandemic influenzain Italy and the impact of various control measures with thehelp of SEIR (Susceptible-Exposed-Infected-Recovered) andindividual-based models Ajelli et al [7] presented the real-time modeling analysis to estimate the impact of the pan-demic and the mitigation measures during the 2009AH1N1v pandemic in Italy Kohlhoff et al [8] carried outan observational study and evaluated hospital massscreening and infection control practices with a pandemicinfluenza full-scale exercise in three acute care hospitals inBrooklyn NY Ventresca and Aleman [9] investigated theeffects of six vaccination strategies in terms of the ability tocontain disease spread by constructing a representativesocial network from the census of the Greater Toronto AreaSchiavo et al [10] presented a review about evidence oninterventions to communicate risk and promote diseasemitigation measures in epidemics Russell et al [11] con-ducted a household survey in a school district of Kentucky toevaluate the effect of school closure mitigation on thetransmission of influenza-like illness Luca et al [12] de-veloped a stochastic spatial age-specific metapopulationalmodel to investigate the impact of school closure on seasonalinfluenza epidemics in Belgium Nicolaides [13] modifiedthe SIR (Susceptible-Infected-Recovered) epidemic model toreflect the effects of hand washing in the infection processand investigated the effect of hand-hygiene mitigationstrategy at airports for flu-type viruses

MCDM methods have been rarely utilized to evaluateinterventions Shin et al [14] used AHP to decide if privateclinics and hospitals or public health centers should offerfree vaccination to children in Korea Mourits et al [15]implemented EVAMIX (evaluations with mixed data) torank control strategies for classical swine fever epidemics inthe EU Aenishaenslin et al [16] implemented D-Sight(PROMETHEE with GAIA) to evaluate prevention andcontrol strategies for the Lyme disease in Quebec CanadaPooripussarakul et al [17] applied best-worst scaling toevaluate vaccines in ailand Previously Samanlioglu [1]evaluated influenza intervention strategies in Turkey withfuzzy AHP-VIKOR

In this study various intervention strategies applied bycountries in the world during the COVID-19 pandemic areevaluated by seven physicians with different expertise actingas consultants and decision makers (DMs) For pairwisecomparison of importance of strategies as the MCDMmethod hesitant F-AHP is applied With (hesitant fuzzy)AHP utilizing pairwise comparisons of alternatives andconsistency check of these comparisons dependable alter-native scores can be determined In this research hesitantF-AHP is preferred over AHP or fuzzy AHP (F-AHP) sincedifferent from AHP with F-AHP the uncertainty andvagueness on DMsrsquo judgments can also be capturedMoreover with the usage of multiple linguistic expressionsand ldquohesitantrdquo terminologies in hesitant F-AHP moreflexibility is attained in decision making than F-AHP since

the degree of hesitation that DMs might have in reality canalso be reflected

2 Literature Review

In AHP [18] with its multilevel and hierarchical structurealternatives are evaluated with respect to each criterion withpairwise comparisons and ranked based on a total weightedscore To reflect the obscurity and fuzziness of DMsrsquojudgments utilizing the concepts of fuzzy set theory [19 20]F-AHP was developed and is used in many MCDM prob-lems in the literature [21ndash24] Fuzzy set theory containsclasses with unsharp boundaries [25 26] and crisp theorysets can be fuzzified by implementing the fuzzy set concepts[19] In the literature different extensions of fuzzy sets suchas intuitionistic fuzzy sets [27 28] Pythagorean fuzzy sets[29ndash31] picture fuzzy sets [32ndash35] spherical fuzzy sets[36ndash43] and hesitant fuzzy sets [44ndash47] were used to dealwith uncertainties in decision making problems

In F-AHP for pairwise comparisons DMs give a singlelinguistic expression and this does not reflect the hesita-tions DMs might have in reality However in hesitantF-AHP DMmight utilize hesitant fuzzy set (HFS) concepts[44 45] hesitant fuzzy linguistic term sets (HFLTS)[44 46] and multiple linguistic expressions and ldquohesitantrdquoterminologies in their evaluations which increase theflexibility and accuracy of the decision making process [47]For example while comparing interventions 1 and 8pairwise DM might give the following assessment ldquoin-tervention 1 is between absolutely strong and very strong incomparison to criterion 8rdquo

Hesitant F-AHP was implemented in several MCDMproblems in the literature Some of these applications areassessment of suppliers [48] cargo company performance[49] woodwork manufacturing CNC routers [50] sus-tainability of hydrogen production methods [51] summersport schools [52] power generation enterprises [47] andinnovation projects [53]

Until now to the best of the authorsrsquo knowledge hesitantF-AHP has never been studied for the evaluation of inter-vention strategies With the proposed hesitant F-AHPimportance of countriesrsquo COVID-19 intervention strategiesis systematically evaluated Application steps of hesitantF-AHP are explained in Section 3 An illustrative study isgiven in Section 4 to demonstrate the implementation alongwith the conclusion and discussion in Section 5

3 Proposed Hesitant F-AHP Approach

In the proposed hesitant F-AHP triangular fuzzy numbers(TFNs) are implemented due to their uncomplicatedness Afuzzy number is a special fuzzy set F (x μF(x)) x isin R1113864 1113865where R minus infinltxlt+infin and μF(x) is from R to [0 1] ATFN 1113957M (l m u)llemle u has the triangular type mem-bership function

Journal of Healthcare Engineering 3

μF(x)

0 xlt l

x minus l

m minus l llexlem

u minus x

u minus m mle xle u

0 xgt u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

Arithmetic operations between two positive TFNs1113957C (l1 m1 u1) 1113957D (l2 m2 u2)l1 lem1 le u1l2 lem2 le u2 anda crisp number E are explained as [53ndash55]

1113957C + 1113957D l1 + l2 m1 + m2 u1 + u2( 1113857

1113957C + E l1 + E m1 + E u1 + E( 1113857

1113957C minus 1113957D l1 minus u2 m1 minus m2 u1 minus l2( 1113857

1113957C minus E l1 minus E m1 minus E u1 minus E( 1113857

1113957Clowast 1113957D l1 lowast l2 m1 lowastm2 u1 lowast u2( 1113857

1113957ClowastE l1 lowastE m1 lowastE u1 lowastE( 1113857 forEge 0

1113957C

1113957D

l1

u2m1

m2u1

l21113888 1113889

1113957C

1113957D min

l1

l2

l1

u2u1

l2u1

u21113888 1113889

m1

m2 max

l1

l2

l1

u2u1

l2u1

u21113888 11138891113888 1113889

(2)

if 1113957C and 1113957D are two TFNs (not necessarily positive TFNs)

1113957C

E

l1

Em1

Eu1

E1113888 1113889 forEgt 0

1113957Cminus 1

1u1

1

m11l1

1113888 1113889

MAX(1113957C + 1113957D) max l1 l2( 1113857 max m1 m2( 1113857 max u1 u2( 1113857( 1113857

MIN(1113957C + 1113957D) min l1 l2( 1113857 min m1 m2( 1113857 min u1 u2( 1113857( 1113857

(3)

For defuzzification of TFNs ldquothe graded mean inte-gration approachrdquo [56] is applied as

Crisp(1113957C) 4m1 + l1 + u1( 1113857

6 (4)

In Triangular Fuzzy Hesitant Fuzzy Sets (TFHFS) themembership degree of an element to a given set is expressedby several possible TFNs Several aggregation operators forTFHFS were introduced by Yu [57] for assessment ofteaching quality

If X is a fixed set the HFS on X returns a subset of [0 1]

by

G ltx hG(x)gt1113868111386811138681113868 x isin X1113966 1113967 (5)

where hG(x) is the possible membership degrees of elementx isin X to set G with values in [0 1] e lower and upperbounds are calculated as

hminus(x) min h(x)

h+(x) max h(x)

(6)

Basic operations for 3 HFS h h1 h2 are given as

hu

⋃

cisinhc

u

1113882 1113883

u

h ⋃

cisinh1 minus (1 minus c)

u

1113882 1113883

h1 plusmn h2 ⋃

c1isinh1c2isinh2c1

+ c2

minus c1c2

1113966 1113967

h1cap h2 ⋃

c1isinh1c2isinh2min c

1 c

21113966 1113967

h1⋃h2 ⋃

c1isinh1c2isinh2max c

1 c

21113966 1113967

h1 otimes h2 ⋃

c1isinh1c2isinh2c1c2

1113966 1113967

(7)

ldquoOrdered Weighting Averaging (OWA)rdquo operator thatcan be employed is

OWA a1 a2 an( 1113857 1113944

n

j1wjbj (8)

where bj is the jth largest of a1 a2 anwj isin [0 1]forallj and1113936

nj1 wj 1 [53 58]

31 Fuzzy Envelope Approach in Hesitant F-AHP ldquoFuzzyenvelope approachrdquo [59] is applied to combine DM evalu-ations in hesitant F-AHP Scales given for DM evaluationsare sorted from the lowest so to the highest sg so if the DMrsquosevaluations are between si and sj then so le si le sj le sg

Based on the HFLTS linguistic expressions can berepresented by a triangular fuzzy membership function 1113957A

(a b c) where a b and c are calculated as

a min aiL a

iM a

i+1M middot middot middot a

jM a

jR1113966 1113967 a

iL (9)

b a

iMifi + 1 j

OWAW aiM a


jM1113966 1113967 otherwise

⎧⎨

⎩ (10)

c max aiL a

iM a


jM a

jR1113966 1113967 a

jR (11)

Weight vector in OWA operator [60] is defined as

w1 αnminus 1 w2 (1 minus α)αnminus 2

middot middot middot wn (1 minus α) (12)

where α (l minus j + i)(l minus 1)Here l depends on the number of terms in DMrsquos

evaluation scale (in Table 2) j is the rank of the highest and iis the rank of the lowest evaluation value i and j can takeranks starting from 0 to l and n j minus i [53 58]


In the proposed hesitant F-AHP approach the DMsmake pairwise comparisons of importance of interventionstrategy alternatives using the linguistic terms given inTable 2

Steps of the proposed hesitant F-AHP are as follows

Step 1 Identify K DMs n alternatives (interventionstrategies) and linguistic terms and scale for thepairwise comparison of alternatives Each DM makespairwise comparison of alternatives (interventionstrategies) with respect to the importance criterionBased on the scale used in Table 2 and utilizingequations (8)ndash(12) DMrsquos assessments are combinedwith fuzzy envelope approach and TFNs corre-sponding to the assessment of each DM are obtainedCalculate

1113957xij 1K

1113957x1ij(+) 1113957x

2ij(+) middot middot middot (+)1113957x

Kij1113872 1113873 (13)

where 1113957xKij (aK

ij bKij cK

ij)foralli j k is the TFN corre-sponding to the evaluation of the Kth DMStep 2

1113957X

(1 1 1) 1113957x12 1113957x1n

1113957x21 (1 1 1) 1113957x2n

1113957xn1 1113957xn2 (1 1 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(14)

with elements 1113957xij (aij bij cij) being then defuzzifiedwith equation (4) and approximate alternative scoresw (w1 w2 wn) being determined by averaging theentries on each row of normalized X erefore thenormalized principal eigenvector is w e largest ei-genvalue (principal eigenvalue λmax) is determinedwith

XwT

λmaxwT (15)

e consistency index (CI) is

CI λmax minus n

n minus 1 (16)

e consistency ratio (CR) is then used to assess theconsistency of pairwise comparisons

CR CI

RI (17)

RI is the random index and if CRlt 010 the com-parisons are consistent and acceptable otherwise theyare not [18]Step 3 If comparisons are acceptable rank the alter-natives (intervention strategies) from the best to theworst based on approximate alternative scoresw (w1 w2 middot middot middot wn) in decreasing order Note thathigher w shows better alternative

4 Illustrative Study

In this study 15 intervention strategies (A1 middot middot middot A15) appliedby countries worldwide during the COVID-19 pandemic areevaluated and compared in terms of the importance crite-rion by 7 physicians who act as DMs In this study DMs are aprofessor of infectious diseases and clinical microbiology(DM1) an infectious disease physician (DM2) a clinicalmicrobiology physician (DM3) two internal medicinephysicians (DM4 and DM5) a family physician (DM6) andan anesthesiology and reanimation physician (DM7) inTurkey

In the proposed hesitant F-AHP 7 DMs compare in-tervention strategy alternatives pairwise with the help oflinguistic terms in Table 2 and the comparison is given inTable 3 After the combination of each DMrsquos assessmentswith ldquofuzzy envelope approachrdquo and aggregation of thecorresponding TFNs of 7 DMs assessments the fuzzyevaluation matrix for the alternative scores ( 1113957X) in Table 4 isobtained

en elements of X are defuzzified with equation (4)and evaluation matrix X in Table 5 is obtained Afterwardsw (w1 w2 wn) is determined by taking the average ofthe entries on each row of normalized X λmax and CR of X

is checked with equations (15)ndash(17) as CI (16268ndash15)14 00906 and CRCIRI 00906159 005698 SinceCRlt 01 the pairwise comparisons are consistent andacceptable

Based on the w (w1 w2 wn) obtained with hesitantF-AHP intervention strategy alternatives are ranked interms of importance criterion from the best to the worst asfollows declaration of emergency (A15) quarantinelock-down of patients and those suspected of infection (A1)curfew (A13) common health testing (independent ofsuspected infection) (A12) social distancing (A3) closure ofschools (A9) external border restrictions reducing theability to exit or enter a country (A8) internal border re-strictions reducing the ability to move freely (trans-portation) within a country (A2) restrictions of massgatherings (A7) health monitoring (A4) restriction ofnonessential government services (A14) government poli-cies that affect the countryrsquos health resources (materials andhealth worker) (A10) formation of new task unitsbureaus

Table 2 Scale for the evaluation of importance of interventionstrategy alternatives in hesitant F-AHP [53]

Linguistic terms Triangular fuzzy number (TFN)Absolutely strong (AS) (2 52 3)Very strong (VS) (32 2 52)Fairly strong (FS) (1 32 2)Slightly strong (SS) (1 1 32)Equal (E) (1 1 1)Slightly weak (SW) (23 1 1)Fairly weak (FW) (12 23 1)Very weak (VW) (25 12 23)Absolutely weak (AW) (13 25 12)


Table 3 Pairwise comparison of importance of COVID-19 intervention strategies by 7 DMs

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15

A1

E FS FW FS FS VS E FS AW E E AW AW FS FW

E VS VS AS-VS VS-FS VS SS SS E E SS SW-

FW FW-VW FW VW

E AS AS AS AS AS AS AS AS AS AS AS AS AS ASE AS FS AS FS-SS FS AS AS AS AS-FS FS AS FS-SS FS FS-SSE VS AS AS AS VS VS SS VS SS E SS FW E AWE AS AS AS AS AS AS AS-VS SS E SS E E FS EE FS-SS FW FS VS AS SS-E E FW SW-FW VS FS VS-FS VS AW

A2

E SW FS FS SW SW E AW SW FW AW AW FW FWE SW-E E SW SW FW FW VW E SW VW VW VW AWE VS VS AS E E E E-SW FW SW-FW VW E-SW E-SW FWE FS SS SS-VS AS FS AS AS AS-FS FS AS FS-SS FS FSE SW SW SS SW SW FW SW E SS SS FW SW VWE SW FW FW FS E-SW E E E SS E E E FWE VS FS AS VS-FS SS E-SW FS VS FS VS-FS SS-E FS SS-E

A3

E VS AS VS AS FS E FS FS E E FS FS

E VS VS-FS FS SS SS FW SW SW AW AW SW AW

E SW-FW FS E-SW SW SW-FW SW-FW FW SW FW FW FW FW-VW

E FS-AS SS-FS AS FS FS-SS SS SS SS FW AS FS FSE SS VS E E SW E SS SS AS SW E SWE E VS FS E E E SS FS E FW FS SW-FWE VS VS VS SS-E FW E-SW VS AS FS FS-SS VS SS-E

A4

E E SW SW FW VW FW SW VW AW SW AWE SS SW SW-E FW SW SW FW AW AW VW AWE AS AS SS SS-E FS E E E SS-E SS-E EE FS FS FS FS-SS FS FS SS FS SW SW SWE SS SW SW FW SW SS E VS SW SW VWE AS AS VS E E SS FS-SS E E FS E

E SS-E SS-E FW-VW

FW-AW VW SS FS SS SW-FW FS AW

A5

E E FW FW AW AW VW AW AW SW AWE E SW SW FW FW FW AW AW VW AW

E SW FW SW SW SW-FW SW FW-VW FW-VW FW FW-VW

E FS SS FS FS SS SS SW SS FS SSE SW SW AW SW SS SS FS SW SW AWE FW FW FW VW FW E VW AW FW VWE E-SW VW AW VW SS-E FS VS SS SW AW

A6

E E E AW FW FW AW AW E AWE SW-E E FW SW-E VW AW AW FW AWE E-SW FS SS E E E FW-VW E FW-VW

E SW FW AW-VW SW SS VW FW E FW

E SW AW SW SS SS FS SW SW AWE FW VW FW FW SW FW VW E FW-VW

E SW-FW VW FW E-SW E VW VW SW AW

A7

E FS SW FS E VW AW FS AWE SW-E E SW FW VW AW SW AWE VS FS-SS E E E FW E VWE FW E SW SS SW FW E FWE SW E SS SW FS FW E VWE E E SW SS SW SW E FWE E-SW E VS AS-VS VS VS VS SS-E


Table 3 Continued


A8

E FW SW FW AW AW VW AWE E SS SS VW VW E VWE E SW SW FW FW-VW SW VWE SS FS SS SW E E EE AS FS FS AS VS AS SSE E SS SS-FS FW SW E SW

E AS-VS VS AS VS FS AS-VS SS-E

A9

E VS VS SW AW VS AWE VS VS VW SW E FWE FW-SW FW-SW VW VW SW-E VWE FS FS E SS FS EE SS SW FS SW E VWE SW SS SW E E SWE VS AS FS FS-SS FS SW-FW

A10

E E AW AW FW AWE E FW VW VW AWE E E E SS-E EE E FW FS FS EE SW SS SW SW SWE E SW SW SS SWE FS FW FW-VW FW AW

A11

E AW AW FW AWE FW FW VW AWE E E E EE E SS FS EE SS SW SW FWE FW SW E FWE VW FW-VW FW AW

A12

E AS AS ASE VS VS EE E SS-E EE E AS ASE FW FW AWE E SS EE SW-FW FS-SS FW

A13

E AS AWE FS FWE FS EE AS EE VS SWE FS FW

E AS-VS E-SW

A14

E AWE FWE SWE FWE SWE SW-FW

E VW-AW

A15

EEEEEE


Table 4 e fuzzy evaluation matrix for the intervention strategy alternatives ( 1113957X)

A1 A2 A3 A4 A5A1 (1000 1000 1000) (1571 2000 2571) (1357 1763 2214) (1643 2143 2714) (1500 1929 2571)A2 (0399 0506 0691) (1000 1000 1000) (0954 1357 1571) (0953 1239 1571) (1167 1586 2000)A3 (0556 0767 1024) (0757 0810 1191) (1000 1000 1000) (1143 1586 2000) (1357 1786 2429)A4 (0379 0477 0667) (0724 0906 1167) (0601 0735 1001) (1000 1000 1000) (1286 1500 1929)A5 (0399 0506 0739) (0604 0846 1071) (0419 0534 0787) (0595 0781 0857) (1000 1000 1000)A6 (0384 0481 0644) (0747 0796 1143) (0590 0677 0906) (0690 0781 1071) (0929 1024 1357)A7 (0532 0671 0739) (0881 1024 1357) (0738 0867 1000) (0796 0953 1381) (1024 1357 1786)A8 (0548 0696 0810) (0904 1057 1286) (0810 0977 1357) (0881 1371 1714) (1214 1524 2000)A9 (0819 1043 1239) (1047 1224 1571) (0953 1071 1357) (1000 1191 1571) (1214 1524 2000)A10 (0762 0863 1071) (0819 0949 1167) (0701 0953 1167) (0787 1024 1214) (1001 1357 1714)A11 (0653 0796 0881) (0763 0977 1357) (0667 0820 1071) (0810 0977 1214) (0906 1167 1429)A12 (0833 0996 1286) (1057 1343 1643) (0976 1224 1500) (1010 1239 1453) (1200 1524 2024)A13 (0890 1153 1571) (1095 1381 1714) (0976 1224 1571) (1238 1429 1857) (1334 1714 2143)A14 (0604 0773 1024) (0929 1120 1500) (0700 0859 1167) (0881 1049 1429) (1000 1239 1714)A15 (1190 1510 1857) (1095 1524 1929) (0952 1191 1714) (1500 1786 2143) (1596 2071 2571)



Table 5 X and intervention strategy alternative scores (w)

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 w

A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604


and government policies changing administrative capacityto respond to the crisis (A11) public awareness campaigns(A5) and restriction of nonessential businesses (A6)

5 Conclusion and Discussion

In this paper a hesitant F-AHP approach is presented tohelp DMs such as policymakers governors and physiciansevaluate and rank intervention strategy alternatives appliedby various countries during the COVID-19 pandemic Atpresent there does not appear to be a study in the literaturethat evaluates countriesrsquo COVID-19 intervention strategiesMoreover in the literature a systematic MCDM approachsuch as hesitant F-AHP has never been utilized to evaluateand rank COVID-19 intervention strategies Adoption ofhesitant fuzzy linguistic terms in the process captures thefuzziness and hesitations and provides flexibility in decisionmaking

In the literature AHP is mainly criticized due to thepossible occurrence of rank reversal phenomenon caused byadding or deleting an alternative [61ndash64] Adding a newalternative includes new information in the model andtherefore the decision needs to be reevaluated [65] Un-fortunately the rank reversal problem occurs not only inAHP but also in many other decision making approachessuch as BordandashKendall method SAW TOPSIS and cross-efficiency evaluation method [61] However this limitationdid not affect our analysis since we did not need to add ordelete any new intervention alternatives

For the illustrative study expert opinion for the eval-uations was needed so a professor of infectious diseases andclinical microbiology an infectious disease physician aclinical microbiology physician two internal medicinephysicians a family physician and an anesthesiology andreanimation physician in Turkey acted as DMs Based ontheir evaluation declaration of emergency quarantinelockdown of patients and those suspected of infection andcurfew are determined as the best three interventionstrategies among the evaluated ones

In this research intervention strategies are evaluatedwithout taking into consideration the interventionsrsquo timingIn reality the timing of the intervention with respect to thebeginning and peak of the epidemic and duration of theapplication of the intervention are really significanterefore when making decisions DMs need to take thoseinto consideration as well as intervention strategy rankingsBased on these the proposed hesitant F-AHP approach can

be adopted and utilized by policy makers governors na-tional public health departments and physicians for theevaluation of countriesrsquo intervention strategies for COVID-19 and other future similar epidemics Also for future re-search various other potentially conflicting quantitative andqualitative criteria can be taken into consideration andinteractions dependencies and feedback relationships be-tween them can be investigated with hesitant fuzzy analyticnetwork process (hesitant F-ANP)

Data Availability

All the data used to support the findings of this study areincluded within the article

Conflicts of Interest

e author declares that there are no conflicts of interestregarding the publication of this article

Acknowledgments

e authors would like to thank Prof Dr Onder ErgonulMD MPH (infectious diseases) Burak Komurcu MD(infectious diseases) Leyla Genccedil MD (clinical microbiol-ogy) Murat Gorgulu MD (internal medicine) TugbaOzturk MD (internal medicine) Alp Ozer MD (familyphysician) and Sezer Yakupoglu MD (anesthesiology andreanimation) for their collaboration in this research

References

[1] F Samanlioglu ldquoEvaluation of influenza intervention strat-egies in Turkey with fuzzy AHP-VIKORrdquo Journal ofHealthcare Engineering vol 2019 Article ID 9486070 9 pages2019

[2] R M Anderson H Heesterbeek D Klinkenberg andT D Hollingsworth ldquoHow will country-based mitigationmeasures influence the course of the COVID-19 epidemicrdquo3e Lancet vol 395 no 10228 pp 931ndash934 2020

[3] H C Johnson C M Gossner E Colzani et al ldquoPotentialscenarios for the progression of a COVID-19 epidemic in theEuropean Union and the European Economic Area March2020rdquo Eurosurveillance vol 25 no 9 pp 1ndash5 2020

[4] C Cheng J Barcelo A S Hartnett and R Kubinec Coro-naNet A Dyadic Dataset of Government Responses to theCOVID-19 Pandemic SocArXiv Ithaca NY USA pp 1ndash622020

Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938


[5] J E Aledort N Lurie J Wasserman and S A BozzetteldquoNon-pharmaceutical public health interventions for pan-demic influenza an evaluation of the evidence baserdquo BMCPublic Health vol 7 no 1 pp 1ndash9 2007

[6] M L Ciofi degli Atti S Merler C Rizzo et al ldquoMitigationmeasures for pandemic influenza in Italy an individual basedmodel considering different scenariosrdquo PLoS One vol 3no 3 Article ID e1790 2008

[7] M Ajelli S Merler A Pugliese and C Rizzo ldquoModel pre-dictions and evaluation of possible control strategies for the2009 AH1N1v influenza pandemic in Italyrdquo Epidemiologyand Infection vol 139 no 1 pp 68ndash79 2011

[8] S A Kohlhoff B Crouch P M Roblin et al ldquoEvaluation ofhospital mass screening and infection control practices in apandemic influenza full-scale exerciserdquo Disaster Medicineand Public Health Preparedness vol 6 no 4 pp 378ndash3842012

[9] M Ventresca and D Aleman ldquoEvaluation of strategies tomitigate contagion spread using social network characteris-ticsrdquo Social Networks vol 35 no 1 pp 75ndash88 2013

[10] R Schiavo M May Leung and M Brown ldquoCommunicatingrisk and promoting disease mitigation measures in epidemicsand emerging disease settingsrdquo Pathogens and Global Healthvol 108 no 2 pp 76ndash94 2014

[11] E S Russell Y Zheteyeva H Gao et al ldquoReactive schoolclosure during increased influenza-like illness (ILI) activity inWestern Kentucky 2013 a field evaluation of effect on ILIincidence and economic and social consequences for fami-liesrdquo Open Forum Infectious Diseases vol 3 no 3 2016

[12] G D Luca K V Kerckhove P Coletti et al ldquoe impact ofregular school closure on seasonal influenza epidemics adata-driven spatial transmission model for Belgiumrdquo BMCInfectious Diseases vol 18 no 1 pp 1ndash16 2018

[13] C Nicolaides D Avraam L Cueto-FelguerosoM C Gonzalez and R Juanes ldquoHand-hygiene mitigationstrategies against global disease spreading through the airtransportation networkrdquo Risk Analysis vol 40 no 4pp 723ndash740 2019

[14] T Shin C-B Kim Y-H Ahn et al ldquoe comparativeevaluation of expanded national immunization policies inKorea using an analytic hierarchy processrdquo Vaccine vol 27no 5 pp 792ndash802 2009

[15] M C M Mourits M A P M van Asseldonk andR B M Huirne ldquoMulti Criteria Decision Making to evaluatecontrol strategies of contagious animal diseasesrdquo PreventiveVeterinary Medicine vol 96 no 3-4 pp 201ndash210 2010

[16] C Aenishaenslin V Hongoh H D Cisse et al ldquoMulti-cri-teria decision analysis as an innovative approach to managingzoonoses results from a study on Lyme disease in CanadardquoBMC Public Health vol 13 no 1 pp 1ndash16 2013

[17] S Pooripussarakul A Riewpaiboon D BishaiC Muangchana and S Tantivess ldquoWhat criteria do decisionmakers in ailand use to set priorities for vaccine intro-ductionrdquo BMC Public Health vol 16 no 1 pp 1ndash7 2016

[18] T L Saaty 3e Analytic Hierarchy Process McGraw-HillNew York NY USA 1980

[19] L A Zadeh ldquoFuzzy logic neural networks and soft com-putingrdquo Communications of the ACM vol 37 no 3pp 77ndash84 1994

[20] H-J Zimmermann ldquoFuzzy logic for planning and decisionmakingrdquo F A Lootsma Ed p 195 Kluwer AcademicPublishers Dordrecht Netherlands 1997

[21] P Srichetta and W urachon ldquoApplying fuzzy analytichierarchy process to evaluate and select product of notebook

computersrdquo International Journal of Modeling and Optimi-zation vol 2 no 2 pp 168ndash173 2012

[22] D Choudhary and R Shankar ldquoAn STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermalpower plant location a case study from Indiardquo Energy vol 42no 1 pp 510ndash521 2012

[23] S Avikal P K Mishra and R Jain ldquoA Fuzzy AHP andPROMETHEE method-based heuristic for disassembly linebalancing problemsrdquo International Journal of ProductionResearch vol 52 no 5 pp 1306ndash1317 2013

[24] G Kabir and R S Sumi ldquoPower substation location selectionusing fuzzy analytic hierarchy process and PROMETHEE acase study from Bangladeshrdquo Energy vol 72 pp 717ndash7302014

[25] F A Lootsma Fuzzy Logic for Planning and Decision MakingSpringer New York NY USA 1997

[26] G J Klir and B Yuan Fuzzy Sets and Fuzzy Logic 3eory andApplications Springer New York NY USA 1st edition 1995

[27] Z Xu and R R Yager ldquoSome geometric aggregation operatorsbased on intuitionistic fuzzy setsrdquo International Journal ofGeneral Systems vol 35 no 4 pp 417ndash433 2006

[28] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 no 1 pp 87ndash96 1986

[29] H Garg ldquoNew logarithmic operational laws and their ag-gregation operators for Pythagorean fuzzy set and their ap-plicationsrdquo International Journal of Intelligent Systemsvol 34 no 1 pp 82ndash106 2019

[30] X Zhang and Z Xu ldquoExtension of TOPSIS to multiple criteriadecision making with pythagorean fuzzy setsrdquo InternationalJournal of Intelligent Systems vol 29 no 12 pp 1061ndash10782014

[31] R R Yager ldquoPythagorean fuzzy subsetsrdquo in Proceedings of theJoint IFSA World Congress and NAFIPS Annual Meeting(IFSANAFIPS) pp 57ndash61 Edmonton Canada June 2013

[32] B C Cuong and V Kreinovich ldquoPicture fuzzy sets-a newconcept for computational intelligence problemsrdquo in Pro-ceedings of the 3ird World Congress on Information andCommunication Technologies (WICT 2013) pp 1ndash6 HanoiVietnam December 2013

[33] T Nucleus S Ashraf T Mahmood S Abdullah andQ Khan ldquoPicture fuzzy linguistic sets and their applicationsfor multi-attribute group decision making problemsrdquo 3eNucleus vol 55 no 2 pp 66ndash73 2018

[34] S Zeng S Asharf M Arif and S Abdullah ldquoApplication ofexponential Jensen picture fuzzy divergence measure inmulti-criteria group decision makingrdquo Mathematics vol 7no 2 p 191 2019

[35] S Ashraf T Mahmood S Abdullah and Q Khan ldquoDifferentapproaches to multi-criteria group decision making problemsfor picture fuzzy environmentrdquo Bulletin of the BrazilianMathematical Society New Series vol 50 no 2 pp 373ndash3972019

[36] S Ashraf S Abdullah and TMahmood ldquoGRAmethod basedon spherical linguistic fuzzy Choquet integral environmentand its application in multi-attribute decision-makingproblemsrdquoMathematical Sciences vol 12 no 4 pp 263ndash2752018

[37] S Ashraf S Abdullah T Mahmood F Ghani andT Mahmood ldquoSpherical fuzzy sets and their applications inmulti-attribute decision making problemsrdquo Journal of Intel-ligent amp Fuzzy Systems vol 36 no 3 pp 2829ndash2844 2019

[38] S Ashraf S Abdullah and T Mahmood ldquoSpherical fuzzyDombi aggregation operators and their application in groupdecision making problemsrdquo Journal of Ambient Intelligence


and Humanized Computing vol 11 no 7 pp 2731ndash27492020

[39] S Ashraf S Abdullah and L Abdullah ldquoChild developmentinfluence environmental factors determined using sphericalfuzzy distance measuresrdquo Mathematics vol 7 no 8 p 6612019

[40] S Ashraf S Abdullah M Aslam M Qiyas and M A KutbildquoSpherical fuzzy sets and its representation of spherical fuzzyt-norms and t-conormsrdquo Journal of Intelligent amp FuzzySystems vol 36 no 6 pp 6089ndash6102 2019

[41] H Jin S Ashraf S Abdullah M Qiyas M Bano and S ZengldquoLinguistic spherical fuzzy aggregation operators and theirapplications in multi-attribute decision making problemsrdquoMathematics vol 7 no 5 p 413 2019

[42] M Rafiq S Ashraf S Abdullah T Mahmood andS Muhammad ldquoe cosine similarity measures of sphericalfuzzy sets and their applications in decision makingrdquo Journalof Intelligent amp Fuzzy Systems vol 36 no 6 pp 6059ndash60732019

[43] S Ashraf and S Abdullah ldquoSpherical aggregation operatorsand their application in multiattribute group decision-mak-ingrdquo International Journal of Intelligent Systems vol 34 no 3pp 493ndash523 2019

[44] V Torra and Y Narukawa ldquoOn hesitant fuzzy sets and de-cisionrdquo in Proceedings of the IEEE International Conference onFuzzy Systems pp 1378ndash1382 Jeju Island South KoreaAugust 2009

[45] V Torra ldquoHesitant fuzzy setsrdquo International Journal of In-telligent Systems vol 25 no 6 pp andashn 2010

[46] R M Rodriguez L Martinez and F Herrera ldquoHesitant fuzzylinguistic term sets for decision makingrdquo IEEE Transactionson Fuzzy Systems vol 20 no 1 pp 109ndash119 2012

[47] R Li J Dong and D Wang ldquoCompetition ability evaluationof power generation enterprises using a hybrid MCDMmethod under fuzzy and hesitant linguistic environmentrdquoJournal of Renewable and Sustainable Energy vol 10 no 5p 055905 2018

[48] B Oztaysi S C Onar E Bolturk and C Kahraman ldquoHesitantfuzzy analytic hierarchy processrdquo in Proceedings of the 2015IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) Istanbul Turkey August 2015

[49] F Tuysuz and B Simsek ldquoA hesitant fuzzy linguistic termsets-based AHP approach for analyzing the performanceevaluation factors an application to cargo sectorrdquo Complex ampIntelligent Systems vol 3 no 3 pp 167ndash175 2017

[50] A Camci G T Temur and A Beskese ldquoCNC router selectionfor SMEs in woodwork manufacturing using hesitant fuzzyAHP methodrdquo Journal of Enterprise Information Manage-ment vol 31 no 4 pp 529ndash549 2018

[51] C Acar A Beskese and G T Temur ldquoSustainability analysisof different hydrogen production options using hesitant fuzzyAHPrdquo International Journal of Hydrogen Energy vol 43no 39 pp 18059ndash18076 2018

[52] M B Ayhan ldquoAn integrated hesitant fuzzy AHP and TOPSISapproach for selecting summer sport schoolrdquo Sakarya Uni-versity Journal of Science vol 22 no 2 2018

[53] F Samanlioglu and Z Ayag ldquoAn intelligent approach for theevaluation of innovation projectsrdquo Journal of Intelligent ampFuzzy Systems vol 38 no 1 pp 905ndash915 2020

[54] L Anojkumar M Ilangkumaran and V Sasirekha ldquoCom-parative analysis of MCDM methods for pipe material se-lection in sugar industryrdquo Expert Systems with Applicationsvol 41 no 6 pp 2964ndash2980 2014

[55] Z Wu J Ahmad and J Xu ldquoA group decision makingframework based on fuzzy VIKOR approach for machine toolselection with linguistic informationrdquo Applied Soft Comput-ing vol 42 pp 314ndash324 2016

[56] D Yong ldquoPlant location selection based on fuzzy TOPSISrdquo3e International Journal of Advanced Manufacturing Tech-nology vol 28 no 7-8 pp 839ndash844 2005

[57] D Yu ldquoTriangular hesitant fuzzy set and its application toteaching quality evaluationrdquo Journal of Information andComputational Science vol 10 no 7 pp 1925ndash1934 2013

[58] A Basar ldquoHesitant fuzzy pairwise comparison for softwarecost estimation a case study in Turkeyrdquo Turkish Journal ofElectrical Engineering amp Computer Sciences vol 25 no 4pp 2897ndash2909 2017

[59] H Liu and R M Rodrıguez ldquoA fuzzy envelope for hesitantfuzzy linguistic term set and its application to multicriteriadecision makingrdquo Information Sciences vol 258 pp 220ndash2382014

[60] D Filev and R R Yager ldquoOn the issue of obtaining OWAoperator weightsrdquo Fuzzy Sets and Systems vol 94 no 2pp 157ndash169 1998

[61] Y-M Wang and Y Luo ldquoOn rank reversal in decisionanalysisrdquo Mathematical and Computer Modelling vol 49no 5-6 pp 1221ndash1229 2009

[62] V Belton and T Gear ldquoOn a short-coming of Saatyrsquos methodof analytic hierarchiesrdquo Omega vol 11 no 3 pp 228ndash2301983

[63] S Schenkerman ldquoAvoiding rank reversal in AHP decision-support modelsrdquo European Journal of Operational Researchvol 74 no 3 pp 407ndash419 1994

[64] H Alharthi N Sultana A Al-Amoudi and A Basudan ldquoAnanalytic hierarchy process-based method to rank the criticalsuccess factors of implementing a pharmacy barcode systemrdquoPerspectives in Health Information Management vol 12 2015

[65] T L Saaty ldquoGroup decision making and the AHPrdquo in 3eAnalytic Hierarchy Process Springer Berlin Germany 1989


Table 1 COVID-19 intervention strategies and country examples

A1 Quarantinelockdown of patients and those suspected ofinfection

Policies to quarantine or shelter in place for at least 14 days For exampleldquoHong Kong a semiautonomous Chinese region requires travelers fromall countries to self-quarantine for 14 daysrdquo

A2 Internal border restrictions reducing the ability to movefreely (transportation) within a country

Government policies which reduce the ability to move freely within acountry For example in Peru as of March 15 2020 ldquoofficials are alsorestricting the movement of people across provincesrdquo

A3 Social distancingGovernment policies that limit physical contact between individuals to15 meters or 6 feet For example in Germany ldquoa 15 meter (49 feet)distance should be kept at all times when in publicrdquo

A4 Health monitoring

Government policies that seek to monitor the health of individuals whoare afflicted with or who are likely to be afflicted with the coronavirus Forexample ldquoTaiwan CDC monitors all individuals who had traveled toWuhan within 14 days and exhibited a fever or symptoms of upperrespiratory tract infectionsrdquo

A5 Public awareness campaigns

Efforts to disseminate and convey reliable information about COVID-19including ways to prevent or mitigate the health effects of COVID-19 Forexample on March 22 2020 it was announced that ldquothe ProvincialYouth Council in Namibia carried out an intense public awarenesscampaign on methods of disease prevention during which youngassociates distributed pamphlets with statements about the pandemicand ways of preventionrdquo

A6 Restriction of nonessential businesses

Government policies that restrict nonessential commercial activity Forexample in Serbia ldquoas of March 21 2020 the following measures are ineffect supermarkets gas stations restaurants post offices banks andother service providers will be reducing their hours to observe the curfewwith some closing at 6 00 PM or earlier Cafes restaurants and shoppingcenters are closed however food delivery is allowedrdquo

A7 Restrictions of mass gatherings

Government policies that limit the number of people allowed tocongregate in a place For example on March 16 2020 in the UnitedStates ldquothe latest recommendation announced Monday by the federalgovernment to promote social distancing and limit the transmission ofthe coronavirus is no more than 10 people in one placerdquo

A8 External border restrictions reducing the ability to exit orenter a country

Government policies which reduce the ability to access ports of entry toor exit from a country For example ldquoNamibian government suspendsinbound and outbound flights for 30 daysrdquo

A9 Closure of schoolsGovernment policy that closes educational establishments in a countryFor example in Slovakia as of March 12 2020 ldquoall schools andeducational establishments will be shut downrdquo

A10 Government policies that affect the countryrsquos healthresources (materials and health worker)

Government policies which affect the material (eg medical equipmentnumber of hospitals for public health) or human (eg doctors nurses)health resources of a country For example ldquoTaiwan bans exports of facemasks ban extended to the end of April (2020)rdquo or ldquoGovernmentapproves plan to build 60 production lines to make an additional 6million masks per dayrdquo

A11Formation of new task unitsbureaus and governmentpolicies changing administrative capacity to respondto the crisis

Government policy that changes the administrative capacity of a part ofgovernment to respond to the crisis For example on January 20 2020ldquoTaiwan activated the Central Epidemic Command Center (CECC)which mobilizes government funds and military personnel to facilitateface mask productionrdquo

A12 Common health testing (independent of suspectedinfection)

Government policies which seek to sample large populations forcoronavirus regardless of suspected likelihood of affliction withcoronavirus

A13 Curfew

Government policies that limit domestic freedom ofmovement to certaintimes of the day For example in Serbia ldquoas of March 21 2020 thefollowing measures are in effect curfew for all residents with fewexceptions from 800pm to 500am the next dayrdquo

A14 Restriction of nonessential government services

Government policy that restricts nonessential government services Forexample in Malaysia from March 18 2020 to March 31 2020 ldquoallgovernment and private services except those involved in essentialservices such as water electricity power telecommunications postaltransportation fuel finance banking health pharmacy fire portairport security retail and food supply will also be closedrdquo

A15 Declaration of emergencye head of government declares a state of national emergency Forexample on March 15 2020 in South Africa ldquoPresident Ramaphosaannounces national state of disasterrdquo






2 Literature Review








μF(x)

0 xlt l

x minus l

m minus l llexlem

u minus x

u minus m mle xle u

0 xgt u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)


1113957C + 1113957D l1 + l2 m1 + m2 u1 + u2( 1113857

1113957C + E l1 + E m1 + E u1 + E( 1113857





1113957C

1113957D

l1

u2m1

m2u1

l21113888 1113889

1113957C

1113957D min

l1

l2

l1

u2u1

l2u1

u21113888 1113889

m1

m2 max

l1

l2

l1

u2u1

l2u1

u21113888 11138891113888 1113889

(2)


1113957C

E

l1

Em1

Eu1

E1113888 1113889 forEgt 0

1113957Cminus 1

1u1

1

m11l1

1113888 1113889



(3)


Crisp(1113957C) 4m1 + l1 + u1( 1113857

6 (4)



by



hminus(x) min h(x)

h+(x) max h(x)

(6)


hu

⋃

cisinhc

u

1113882 1113883

u

h ⋃


u

1113882 1113883

h1 plusmn h2 ⋃

c1isinh1c2isinh2c1

+ c2

minus c1c2

1113966 1113967

h1cap h2 ⋃


1 c

21113966 1113967

h1⋃h2 ⋃


1 c

21113966 1113967

h1 otimes h2 ⋃


1113966 1113967

(7)


OWA a1 a2 an( 1113857 1113944

n

j1wjbj (8)


nj1 wj 1 [53 58]




a min aiL a

iM a


jM a

jR1113966 1113967 a

iL (9)

b a

iMifi + 1 j

OWAW aiM a



⎧⎨

⎩ (10)

c max aiL a

iM a


jM a

jR1113966 1113967 a

jR (11)










1113957xij 1K

1113957x1ij(+) 1113957x


Kij1113872 1113873 (13)


ij bKij cK


1113957X

(1 1 1) 1113957x12 1113957x1n

1113957x21 (1 1 1) 1113957x2n

1113957xn1 1113957xn2 (1 1 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(14)


XwT

λmaxwT (15)


CI λmax minus n

n minus 1 (16)


CR CI

RI (17)













A1



FW FW-VW FW VW


A2


A3





A4


E SS-E SS-E FW-VW


A5




A6





A7



Table 3 Continued


A8



A9


A10


A11


A12


A13


E AS-VS E-SW

A14


E VW-AW

A15

EEEEEE








A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604









Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938







































































2 Literature Review








μF(x)

0 xlt l

x minus l

m minus l llexlem

u minus x

u minus m mle xle u

0 xgt u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)


1113957C + 1113957D l1 + l2 m1 + m2 u1 + u2( 1113857

1113957C + E l1 + E m1 + E u1 + E( 1113857





1113957C

1113957D

l1

u2m1

m2u1

l21113888 1113889

1113957C

1113957D min

l1

l2

l1

u2u1

l2u1

u21113888 1113889

m1

m2 max

l1

l2

l1

u2u1

l2u1

u21113888 11138891113888 1113889

(2)


1113957C

E

l1

Em1

Eu1

E1113888 1113889 forEgt 0

1113957Cminus 1

1u1

1

m11l1

1113888 1113889



(3)


Crisp(1113957C) 4m1 + l1 + u1( 1113857

6 (4)



by



hminus(x) min h(x)

h+(x) max h(x)

(6)


hu

⋃

cisinhc

u

1113882 1113883

u

h ⋃


u

1113882 1113883

h1 plusmn h2 ⋃

c1isinh1c2isinh2c1

+ c2

minus c1c2

1113966 1113967

h1cap h2 ⋃


1 c

21113966 1113967

h1⋃h2 ⋃


1 c

21113966 1113967

h1 otimes h2 ⋃


1113966 1113967

(7)


OWA a1 a2 an( 1113857 1113944

n

j1wjbj (8)


nj1 wj 1 [53 58]




a min aiL a

iM a


jM a

jR1113966 1113967 a

iL (9)

b a

iMifi + 1 j

OWAW aiM a



⎧⎨

⎩ (10)

c max aiL a

iM a


jM a

jR1113966 1113967 a

jR (11)










1113957xij 1K

1113957x1ij(+) 1113957x


Kij1113872 1113873 (13)


ij bKij cK


1113957X

(1 1 1) 1113957x12 1113957x1n

1113957x21 (1 1 1) 1113957x2n

1113957xn1 1113957xn2 (1 1 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(14)


XwT

λmaxwT (15)


CI λmax minus n

n minus 1 (16)


CR CI

RI (17)













A1



FW FW-VW FW VW


A2


A3





A4


E SS-E SS-E FW-VW


A5




A6





A7



Table 3 Continued


A8



A9


A10


A11


A12


A13


E AS-VS E-SW

A14


E VW-AW

A15

EEEEEE








A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604









Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938



































































μF(x)

0 xlt l

x minus l

m minus l llexlem

u minus x

u minus m mle xle u

0 xgt u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)


1113957C + 1113957D l1 + l2 m1 + m2 u1 + u2( 1113857

1113957C + E l1 + E m1 + E u1 + E( 1113857





1113957C

1113957D

l1

u2m1

m2u1

l21113888 1113889

1113957C

1113957D min

l1

l2

l1

u2u1

l2u1

u21113888 1113889

m1

m2 max

l1

l2

l1

u2u1

l2u1

u21113888 11138891113888 1113889

(2)


1113957C

E

l1

Em1

Eu1

E1113888 1113889 forEgt 0

1113957Cminus 1

1u1

1

m11l1

1113888 1113889



(3)


Crisp(1113957C) 4m1 + l1 + u1( 1113857

6 (4)



by



hminus(x) min h(x)

h+(x) max h(x)

(6)


hu

⋃

cisinhc

u

1113882 1113883

u

h ⋃


u

1113882 1113883

h1 plusmn h2 ⋃

c1isinh1c2isinh2c1

+ c2

minus c1c2

1113966 1113967

h1cap h2 ⋃


1 c

21113966 1113967

h1⋃h2 ⋃


1 c

21113966 1113967

h1 otimes h2 ⋃


1113966 1113967

(7)


OWA a1 a2 an( 1113857 1113944

n

j1wjbj (8)


nj1 wj 1 [53 58]




a min aiL a

iM a


jM a

jR1113966 1113967 a

iL (9)

b a

iMifi + 1 j

OWAW aiM a



⎧⎨

⎩ (10)

c max aiL a

iM a


jM a

jR1113966 1113967 a

jR (11)










1113957xij 1K

1113957x1ij(+) 1113957x


Kij1113872 1113873 (13)


ij bKij cK


1113957X

(1 1 1) 1113957x12 1113957x1n

1113957x21 (1 1 1) 1113957x2n

1113957xn1 1113957xn2 (1 1 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(14)


XwT

λmaxwT (15)


CI λmax minus n

n minus 1 (16)


CR CI

RI (17)













A1



FW FW-VW FW VW


A2


A3





A4


E SS-E SS-E FW-VW


A5




A6





A7



Table 3 Continued


A8



A9


A10


A11


A12


A13


E AS-VS E-SW

A14


E VW-AW

A15

EEEEEE








A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604









Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938






































































1113957xij 1K

1113957x1ij(+) 1113957x


Kij1113872 1113873 (13)


ij bKij cK


1113957X

(1 1 1) 1113957x12 1113957x1n

1113957x21 (1 1 1) 1113957x2n

1113957xn1 1113957xn2 (1 1 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(14)


XwT

λmaxwT (15)


CI λmax minus n

n minus 1 (16)


CR CI

RI (17)













A1



FW FW-VW FW VW


A2


A3





A4


E SS-E SS-E FW-VW


A5




A6





A7



Table 3 Continued


A8



A9


A10


A11


A12


A13


E AS-VS E-SW

A14


E VW-AW

A15

EEEEEE








A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604









Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938





































































A1



FW FW-VW FW VW


A2


A3





A4


E SS-E SS-E FW-VW


A5




A6





A7



Table 3 Continued


A8



A9


A10


A11


A12


A13


E AS-VS E-SW

A14


E VW-AW

A15

EEEEEE








A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604









Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938



































































Table 3 Continued


A8



A9


A10


A11


A12


A13


E AS-VS E-SW

A14


E VW-AW

A15

EEEEEE








A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604









Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938









































































A1 1000 2024 1770 2155 1964 2143 1810 1679 1455 1367 1452 1384 1131 1528 0955 00936A2 0519 1000 1326 1246 1585 1345 1016 1120 1115 1275 1072 1085 0830 1014 0799 00644A3 0775 0865 1000 1581 1821 1635 1302 1013 0917 1199 1365 1114 1059 1306 0957 00704A4 0492 0919 0757 1000 1536 1488 1141 0856 0988 1056 1056 1071 0783 1061 0667 00580A5 0527 0843 0557 0763 1000 1004 0796 0799 0788 0821 0974 0905 0699 0891 0540 00471A6 0492 0845 0701 0814 1064 1000 0882 0804 0708 0902 0903 0719 0577 0941 0493 00464A7 0659 1056 0868 0998 1373 1143 1000 1147 1016 1203 1127 1059 0835 1206 0616 00604









Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938










































































Data Availability




Acknowledgments


References





Table 5 Continued


A8 0690 1070 1013 1347 1552 1528 0994 1000 1338 1294 1282 1108 0990 1291 0791 00680A9 1038 1253 1099 1223 1552 1587 0969 0898 1000 1460 1532 0988 0865 1278 0681 00685A10 0881 0964 0947 1016 1357 1171 0915 0852 0775 1000 1064 0789 0839 0931 0729 00566A11 0786 1005 0836 0989 1167 1210 0987 0896 0760 0969 1000 0770 0806 0907 0658 00545A12 1017 1345 1229 1236 1554 1742 1196 1357 1223 1433 1492 1000 1270 1576 1300 00799A13 1179 1389 1241 1468 1722 1881 1585 1339 1330 1421 1385 0940 1000 1940 0813 00811A14 0787 1151 0884 1084 1278 1095 0899 0989 0855 1239 1254 0773 0549 1000 0688 00572A15 1515 1520 1239 1798 2075 2095 1849 1496 1607 1667 1786 1116 1381 1560 1000 00938



































































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