EvaluationofInfluenzaInterventionStrategiesinTurkeywith...

Research ArticleEvaluation of Influenza Intervention Strategies in Turkey withFuzzy AHP-VIKOR

Funda Samanlioglu

Department of Industrial Engineering Kadir Has University 34083 Cibali Istanbul Turkey

Correspondence should be addressed to Funda Samanlioglu fsamanlioglukhasedutr

Received 8 October 2018 Revised 25 October 2019 Accepted 5 November 2019 Published 19 November 2019

Academic Editor Vincenzo Positano

Copyright copy 2019 Funda Samanliogluis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this study a fuzzy AHP-VIKOR method is presented to help decision makers (DMs) especially physicians evaluate and rankintervention strategies for influenza Selecting the best intervention strategy is a sophisticated multiple criteria decision-making(MCDM) problemwith potentially competing criteria Two fuzzyMCDMmethods fuzzy analytic hierarchy process (F-AHP) andfuzzy VIsekriterijumska optimizacija i KOmpromisno Resenje (F-VIKOR) are integrated to evaluate and rank influenza in-tervention strategies In fuzzy AHP-VIKOR F-AHP is used to determine the fuzzy criteria weights and F-VIKOR is implementedto rank the strategies with respect to the presented criteria A case study is given where a professor of infectious diseases andclinical microbiology an internal medicine physician an ENT physician a family physician and a cardiologist in Turkey act asDMs in the process

1 Introduction

e 2009 A(H1N1) influenza pandemic caused a global alertand all countries implemented various intervention strate-gies Some measures across communities were pharma-ceutical such as antivirals and vaccination and some werenonpharmaceutical such as limiting public gatheringsclosing schools and restricting travel [1 2] Union HealthSecurity Committee recommended to vaccinate risk andtarget groups such as pregnant women healthcare workersand people older than six months with chronic illnesses[3 4] Unless an effective intervention strategy is appliedinfluenza spreads rapidly in seasonal epidemics and costssociety a substantial amount in terms of healthcare expenseslost productivity and loss of life

During the 2009 A(H1N1) influenza pandemic in EUHungary started vaccination first and by July 2010 about 9was vaccinated in EUEEA [3] However in most of thecountries vaccination campaigns were not as effective asplanned due to the timing and the percentage of coverage[5] Norway and Sweden were compared in terms of theirvaccination strategies in a previous study [5] In Swedenvaccination campaign was more effective than Norway Even

though vaccination started almost the same time in bothcountries and although about 40 of population got vacci-nated in Norway it was too late to be effective due to therelative timing of the starting time of vaccination and itslocation in the epidemic wave [5ndash7] As discussed inSamanlioglu and Bilgersquos study [5] for the vaccination cam-paign to be effective vaccination should start in the earlyphases of the epidemic but it does not need to continue overthe peak of the epidemice effect of vaccination timing andsales of antivirals in Norway were analysed and they showedthat the countermeasures only prevented 11-12 of thepotential cases relative to an unmitigated pandemic and thatif the campaign would have started 6 weeks earlier thevaccination alone might have reduced the clinical attack rateby 50 [6] e interventions in France and Germany werediscussed in a previous study and even though Germany andFrance have similar vaccination policies the relative fatalitieswere higher in France [5] e peak of the epidemic wasdelayed in France due to the timing of school holidays [8]edifference can be explained by epidemic-specific precautionsand healthcare procedures applied in Germany [9]

As realized from 2009 A(H1N1) pandemic a systematicapproach is needed for effective health planning and making

HindawiJournal of Healthcare EngineeringVolume 2019 Article ID 9486070 9 pageshttpsdoiorg10115520199486070

decisions related to intervention strategies during an in-fluenza pandemic especially for transparency and ac-countability of the decision-making process Evaluation ofintervention strategies is a significant MCDM problem thatrequires expertise and competency since there are variouspotentially conflicting criteria to take into consideration Inthe literature there are a few studies that utilize MCDMmethods for evaluation of intervention strategies Shin et al[10] used AHP to evaluate the expanded Korean immuni-zation programs and assess two policies weather privateclinics and hospitals or public health centers should offer freevaccination services to children Mourits et al [11] applied theEVAMIX (evaluations with mixed data) MCDM method torank alternative strategies to control classical swine feverepidemics in EU Aenishaenslin et al [12] implementedD-Sight which uses PROMETHEE methods (PreferenceRanking Organization Method for Enrichment Evaluations)and gives access to the GAIA (Geometrical Analysis forInteractive Aid) to assess various prevention and controlstrategies for the Lyme disease in Quebec Canada eydeveloped two MCDM models one for surveillance in-terventions and one for control interventions and conductedthe analysis under a disease emergence and an epidemicscenario Pooripussarakul et al [13] implemented best-worstscaling to assess and rank-order vaccines for introduction intothe expanded program on immunization in ailand

In this study various influenza intervention strategiesare evaluated taking into consideration potentially con-flicting criteria by five physicians with different expertisesacting as consultants and decision makers (DMs) As theMCDMmethod and integrated method fuzzy AHP-VIKORis implemented to evaluate and rank the strategies In fuzzyAHP-VIKOR F-AHP is implemented to find the fuzzycriteria weights and F-VIKOR is utilized to rank alternativesusing these weights Here an integrated method is used tohave both methodsrsquo advantages F-VIKOR is easy to use forMCDM problems with especially conflicting criteria how-ever it does not include guidelines for determining theweights of criteria and with F-AHP through pairwisecomparisons reliable fuzzy weights can be obtained Withthe integrated fuzzy AHP-VIKOR intervention strategiesare ranked without too many repetitive pairwise compari-sons and complicated calculations

e fuzzy set theory is a mathematical theory designed tomodel the vagueness or imprecision of human cognitiveprocesses It is a theory of classes with unsharp boundariesand any crisp theory can be fuzzified by generalizing theconcept of a set within that theory to the concept of a fuzzyset [14] Fuzzy extensions of AHP (F-AHP) and VIKOR (F-VIKOR) are used to capture the uncertainty and vaguenesson judgments of DMs

In AHP [15] alternatives are evaluated based on variouscriteria in a hierarchical and multilevel structure and thenalternatives are ranked based on a calculated total weightedscore AHP is used widely in real-life applications ie fordecisions related to machine shops [16] for evaluation ofmachine tools [17 18] and for evaluation of medical devicesand materials [19] e VIKOR method was introducedmainly for MCDM problems with competing or

noncommensurable criteria In VIKOR compromise rankingis performed and alternatives are compared according to thecloseness to the ideal solution [20ndash23] To reflect the un-certainty and vagueness on judgments of DMs their fuzzyextensions F-AHP and F-VIKOR have been developedWithF-VIKOR an accepted compromise solution is obtained witha maximum group utility of the majority and a minimum ofindividual regret of the opponent [22 24] In the literaturedifferent versions of F-VIKOR exist such as F-VIKOR withTriangular fuzzy numbers [24 25] triangular intuitionisticfuzzy numbers [26] 2-tuple group decision-making linguisticmodel [27] an attitudinal-based interval 2-tuple linguisticmodel [28] type-2 fuzzy model [29 30] and an intuitionistichesitant model using entropy weights [31] Several real-lifeapplications of F-AHP F-VIKOR and fuzzy AHP-VIKORare given in Table 1

At present there does not appear to be a research paperin the literature that focuses on evaluation and ranking ofinfluenza intervention strategies Moreover fuzzy AHP-VIKOR has never been used in the evaluation of in-tervention strategies for a pandemic In the next sectionsfuzzy AHP-VIKOR steps and a case study are presented

2 Proposed Fuzzy AHP-VIKOR Approach

21 Definitions In fuzzy set theory there are classes withunsharp boundaries [61 62] Any crisp theory can be fuz-zified using the concept of a fuzzy set [14] In the proposedfuzzy AHP-VIKOR triangular fuzzy numbers (TFNs) areused due to its simplicity A fuzzy number is a special fuzzyset F (x μF(x)) x isin R1113864 1113865 Here R minus infinlt xlt +infin andμF(x) is from R to [0 1] A TFN denoted as 1113957M (l m u)where llemle u has the membership function

μF(x)

0 xlt l

x minus l

m minus l llexlem

u minus x

u minus m mlexle u

0 xgt u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

Basic operations between two positive TFNs 1113957A (l1

m1 u1) 1113957B (l2 m2 u2) l1 lem1 le u1 l2 lem2 le u2 and acrisp number C(Cge 0) are explained as follows

1113957A + 1113957B l1 + l2 m1 + m2 u1 + u2( 1113857

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

1113957A minus 1113957B l1 minus u2 m1 minus m2 u1 minus l2( 1113857

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

1113957Alowast 1113957B l1 lowast l2 m1 lowastm2 u1 lowastu2( 1113857

1113957AlowastC l1 lowastC m1 lowastC u1 lowastC( 1113857

1113957A

1113957B

l1

u2m1

m2u1

l21113888 1113889

2 Journal of Healthcare Engineering

1113957A

1113957B min

l1

l2

l1

u2u1

l2u1

u21113888 1113889

m1

m2 max

l1

l2

l1

u2u1

l2u1

u21113888 11138891113888 1113889

if 1113957A and 1113957B are TFNs (not neccesarily positive TFNs)

1113957A

C

l1

Cm1

Cu1

C1113888 1113889 for Cgt 0

1113957Aminus 1

1u1

1

m11l1

1113888 1113889

max(1113957A + 1113957B) max l1 l2( 1113857 max m1 m2( 1113857 max u1 u2( 1113857( 1113857

min(1113957A + 1113957B) min l1 l2( 1113857 min m1 m2( 1113857 min u1 u2( 1113857( 1113857

(2)

e gradedmean integration approach [63] is used as thedefuzzification method to convert TFNs into crisp numbersHere

crisp(1113957A) 4m1 + l1 + u1( 1113857

6 (3)

22 Finding the Important Weights of Criteria with F-AHPAfter constructing the hierarchical structure of the prob-lem the DMs make pairwise comparisons of the criteriaand estimate their relative importance in relation to theelement at the immediate proceeding level During the

process of evaluation of criteria the pairwise comparisonsare made by using the linguistic terms and scale presentedin Table 2

221 Computational Steps of F-AHP

Step 1 Form a decision group ofK people Identify n criteriaand select the suitable linguistic terms for the pairwisecomparison of criteria Calculate the aggregated 1113957xij

(1K)(1113957x1ij(+)1113957x2

ij(+) middot middot middot (+)1113957xKij) where 1113957xK

ij (aKij bK

ij cKij)

inwhichforalli j k is the TFN corresponding to the evaluationof the Kth DM

Step 2 1113957X

(1 1 1) 1113957x12 middot middot middot middot middot middot 1113957x1n

1113957x21 (1 1 1) middot middot middot middot middot middot 1113957x2n

middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot


1113957xn1 1113957xn2 middot middot middot middot middot middot (1 1 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with ele-

ments 1113957xij (aij bij cij) is normalized and 1113957S is obtained

1113957S

1113957s11 1113957s12 middot middot middot middot middot middot 1113958s1n




1113957sn1 1113957sn2 middot middot middot middot middot middot 1113957snn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

where 1113957sij (aij1113936icijbij1113936ibij

cij1113936iaij) Fuzzy priority weight vector 1113957wcriteria ( 1113957w1 1113957w2

1113957wn) is calculated by averaging the entries on each row of 1113957S

Table 1 Fuzzy AHP fuzzy VIKOR and fuzzy AHP-VIKOR applications

Fuzzy AHPapplications

(i) Selection of concepts in an NPD environment [32](ii) Evaluation of machine tools in a manufacturing system [33 34](iii) Evaluation of notebook computers for buyers [35](iv) Evaluation of disassembly line balancing solutions [36](v) Selection of power substation locations [37](vi) Selection of thermal power plant locations [38](vii) Selection of biodiesel blend for IC engines [39]

Fuzzy VIKORapplications

(i) Water resources planning [25](ii) Evaluation of the vulnerability of the water supply to climate change and variability in South Korea [40](iii) Material selection in an engineering application [41](iv) Reverse logistics [42](v) Site selection in waste management [28](vi) Evaluation of hospital services in Taiwan [43](vii) Selection of CNC machine tools [44](viii) Evaluation of schoolsrsquo academic performance [45](ix) Selection of green supplier development programs [46](x) Review papers about VIKOR and fuzzy VIKOR applications [47 48](xi) Selection of a managed security service provider [49](xii) Selection of measures for prevention and reduction of ldquosmogrdquo (smoke and fog) in Pakistan [50](xiii) Risk assessment of China-Pakistan fiber optic project (CPFOP) [51]

Fuzzy AHP-VIKORapplications

(i) Selection of the best renewable energy alternative and the best energy production site for Istanbul [52](ii) Selection of machine tool alternative for the manufacturing sector [53](iii) Evaluation of the performance levels of Turkish banks registered in Borsa Istanbul (AHP and F-VIKOR) [54](iv) Ranking the financial performance of several Iranian companies [55](v) Evaluation of performance of Iranian cement firms (F-AHP and VIKOR) [56](vi) Selection of pipe material in sugar industry (F-AHP and VIKOR) [57](vii) Evaluation of busses for public transportation [58](viii) Selection of the best knowledge flow practicing organization [59](ix) Evaluation of compliant polishing tool (AHP and F-VIKOR) [60]

Journal of Healthcare Engineering 3

Step 3 1113957X is defuzzified by using equation (3) and wcr

(w1 w2 wn) (approximate crisp criteria weights) iscalculated by averaging the entries on each row of nor-malized X So the normalized principal eigen vector is wcre largest eigenvalue called the principal eigenvalue (λmax)is determined with the following equation

XwTcr λmaxw

Tcr (4)

emeasure of inconsistency of pairwise comparisons iscalled the consistency index (CI) and it is calculated as

CI λmax minus n

n minus 1 (5)

e consistency ratio (CR) is used to estimate theconsistency of pairwise comparisons and the CR is calcu-lated by dividing CI by the random consistency index (RI)

CR CIRI

(6)

RI is the average index for randomly generated weights[15] If the CR is less than 010 the comparisons are ac-ceptable otherwise they are not

23 Ranking of Alternatives with F-VIKOR In the previoussection fuzzy priority weight vector 1113957wcriteria (1113957w1 1113957w2

1113957wn) was obtained with F-AHP After the determination of1113957wcriteria with F-AHP in order to rank the alternativesF-VIKOR is used During the process of evaluation of al-ternatives with F-VIKOR the linguistic terms and scalepresented in Table 3 is used

231 Computational Steps of F-VIKOR

Step 1 Identify the m alternatives and select the suitablelinguistic terms for the evaluations of alternatives with re-spect to each criterion Calculate the aggregated 1113957rij

(1K)(1113957r1ij(+)1113957r2ij(+) middot middot middot (+)1113957rKij) where 1113957rK

ij (aKij bK

ij ckij) is the

TFN for the evaluation of the Kth DM After the aggregationthe fuzzy MCDM problem with m alternatives that areevaluated in terms of n criteria can be expressed in a fuzzy

matrix format as 1113957D

1113957r11 1113957r12 middot middot middot middot middot middot 1113957r1n



middot middot middot middot middot middot middot middot middot middot middot middot

1113957rn1 1113957rn2 middot middot middot middot middot middot 1113957rmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

where

1113957rij (aij bij cij) foralli j are positive TFNs

Step 2 Find the fuzzy best value (FBV 1113957flowastj ) and the fuzzy

worst value (FWV 1113957fminus

j ) for each criterion

1113957flowastj max

i1113957rij forallj

1113957fminus

j mini

1113957rij forallj(7)

Step 3 Calculate the separation measures of each alternativefrom the FBV (1113957Si) and FWV (1113957Ri)

1113957Si 1113944n

j1

1113957wj1113957flowastj minus 1113957rij1113872 1113873

1113957flowastj minus 1113957f

minus

j1113872 1113873 foralli

1113957Ri maxj



minus

j

⎡⎢⎢⎣ ⎤⎥⎥⎦ foralli

(8)

Step 4 Calculate 1113957Slowast 1113957S

minus 1113957Rlowast and 1113957R

minus values as

1113957Slowast

mini

1113957Si

1113957Sminus

maxi

1113957Si

1113957Rlowast

mini

1113957Ri

1113957Rminus

maxi

1113957Ri

(9)

Step 5 Calculate 1113957Qi values for each alternative

1113957Qi ]1113957Si minus 1113957S

lowast

1113957Sminus

minus 1113957Slowast +(1 minus ])

1113957Ri minus 1113957Rlowast

1113957Rminus

minus 1113957Rlowast foralli (10)

where ] is the weight of the strategy of the maximum grouputility (majority of criteria) and 1 minus ] is the weight of theindividual regret ] is usually assumed to be 05 (by con-sensus) [52 57]

Table 2 Linguistic terms and TFNs for the evaluation of criteria inF-AHP

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 Linguistic terms and TFNs for the ratings of alternatives inF-VIKOR

Linguistic terms Triangular fuzzy number (TFN)Very poor (VP) (0 0 1)Poor (P) (0 1 3)Medium poor (MP) (1 3 5)Fair (F) (3 5 7)Medium good (MG) (5 7 9)Good (G) (7 9 10)Very good (VG) (9 10 10)


Step 6 Defuzzify the 1113957Qi values with equation (3) and rankthe alternatives based on crisp Qi values Consequently thesmaller the Qi the better the alternative

Step 7 Determine a compromise solution Assume that twoconditions below are acceptable en by using Qi a singleoptimal solution A(1) is determined

Condition 1 (acceptable advantage) Q(A(2)) minus Q(A(1))geDQ and DQ 1(m minus 1) but DQ 025 if mlt 4 Here A(1) isthe first ranked alternative and A(2) is the second ranked al-ternative based on crisp Qi values and m is the number ofalternatives

Condition 2 (acceptable stability in decision-making) Q(A(1))

must be S(A(1)) andorR(A(1)) under this condition

If Condition 1 is not accepted and Q(A(m)) minus Q(A(1))

ltDQ then A(m) andA(1) are the same compromise solutionA(1) does not have a comparative advantage so the com-promise solutions A(1) A(2) A(m) are the same If Con-dition 2 is not accepted the stability of decision-making isdeficient although A(1) has a comparative advantage Hencecompromise solutions A(1) andA(2) are same [51 64 65]

3 Case Study

In this study DMs are a professor of infectious diseases andclinical microbiology (DM1) an internal medicine physician(DM2) an ENTphysician (DM3) a family physician (DM4)and a cardiologist (DM5) in Turkey 8 benefit criteria aredetermined by the DMs for the evaluation of influenzaintervention strategies ese are listed in Table 4

e alternatives that are going to be ranked are massvaccination (A1) antiviral treatment and isolation of in-fected individuals (A2) and exclusion of people from highrisk areas (mass measurements to reduce the contact rate ieschool closures and closure of public places) (A3)

In order to determine the fuzzy criteria weights F-AHPis used In F-AHP first DMs do pairwise comparison ofcriteria using the linguistic terms presented in Table 2Comparisons of 5 DMs are presented in Table 5 After theaggregation of the corresponding TFNs of the DMs evalu-ations in Table 6 1113957X is given Afterwards fuzzy priorityweight vector 1113957wcriteria (1113957w1 1113957w2 1113957wn) is calculated byaveraging the entries on each row of normalized 1113957X(1113957S)1113957wcriteria is presented in Table 7 In order to calculate the CR of1113957X equation (3) is utilized for defuzzification CR is de-termined as 00483 and since it is less than 01 the com-parison results are considered to be consistent

1113957wcriteria (1113957w1 1113957w2 1113957wn) determined with F-AHP isused in F-VIKOR to rank intervention alternatives InF-VIKOR first DMs evaluate alternatives with respect toevaluation criteria using the linguistic terms presented inTable 3 ese evaluations are presented in Table 8 After theaggregation of the corresponding TFNs of the DMsrsquo eval-uations in Table 9 1113957D is presented Also in Table 9 the FBV(1113957flowastj ) and the FWV (1113957f

minus

j ) for each criterion are presentedeseparation measures of each alternative 1113957Si and 1113957Ri are given in

Table 10 along with 1113957Slowast 1113957S


minus values Based onthese 1113957Qi value for each alternative is calculated and pre-sented in Table 10 Afterwards 1113957Qi 1113957Si and 1113957Ri values aredefuzzified with equation (3) and ranking of alternativeswith respect to Si Ri andQi are shown in Table 11

Table 4 Evaluation criteria for influenza intervention strategies

C1 Effectiveness (reduction of incidence of cases)C2 Lack of health side effectsC3 Cost-effectiveness

C4 Feasibility and timing (minimum delay beforeresults)

C5 Public acceptance

C6 Equity and availability (proportion of populationbenefitting)

C7 Applicability (easiness and minimum complexity)C8 Lack of unintended effects about work and social life

Table 5 5 DMsrsquo pairwise comparison of evaluation criteria

C1 C2 C3 C4 C5 C6 C7 C8

C1

E AS VS VS AS SS VS FSE AS FS VS VS SS VS VSE E FS VS SS E E SSE VS E SW VW E SW EE AS S VS VS E E SS

C2

E FS VS FS FS FS FSE FS FS SS SS SS EE FS SS AS SW FW SWE VS SS SS SS E FSE FS FS AS SS FS FS

C3

E FS VW FS E EE FS SS FS E FSE E VS E SW VWE FS SW E E FSE SS FW SS E E

C4

E FW FS E EE SW VS SS EE SS E SS FWE SW SW SW SWE SW FS E E

C5

E VS FS FSE AS FS VSE VS VS VSE FW FS FSE VS VS SS

C6

E E EE SS EE E VWE FS FSE E E

C7

E EE SSE EE VSE E

C8

EEEEE


Consequently the smaller the Qi the better the alter-native so based on Qi alternatives are ranked from best toworst as mass vaccination (A1) antiviral treatment andisolation of infected individuals (A2) and exclusion of peoplefrom high risk areas (mass measurements to reduce thecontact rate ie school closures closure of public places etc)(A3) However to determine a compromise solution Con-ditions 1 and 2 are checked Condition 1 (acceptable ad-vantage) is not satisfied when A1 and A2 are compared sinceQ(A(2)) minus Q(A(1)) 0171 minus 0085 0086ltDQ 025

Condition 2 (acceptable stability in decision-making) issatisfied since Q(A(1)) is also R(A(1)) as shown in Table 11Compromise solutions A1 and A2 are the same SinceQ(A(3)) minus Q(A(1)) 0639 minus 0085 0555geDQ 025 A3and A1 are not the same compromise solution and A1 hasacceptable advantage over A3 Also A1 is better ranked thanA3 in terms of Si andRi values as shown in Table 11 so thereis acceptable stability in decision-making Since Q(A(3))minus

Q(A(2)) 0639 minus 0171 0468geDQ 025 A3 and A2 arenot the same compromise solution and A2 has acceptable

Table 6 Fuzzy evaluation matrix for the criteria weights ( 1113957X)

C1 C2 C3 C4 C5 C6 C7 C8

C1 (1000 10001000)

(1700 21002500)

(0900 12001500)

(1334 18002200)

(1280 16002034)

(1000 10001200)

(1134 14001600)

(1100 13001700)

C2 (0478 05400634)

(1000 10001000)

(1100 16002100)

(1100 14001900)

(1400 17002200)

(0934 11001500)

(0900 11341500)

(0934 13001600)

C3 (0480 05680734)

(0480 06360934)

(1000 10001000)

(1000 13001700)

(0814 10341334)

(1000 12001500)

(0934 10001000)

(0880 11001334)

C4 (0520 06000836)

(0548 07680934)

(0634 08021000)

(1000 10001000)

(0702 09341100)

(1034 14001700)

(0934 10001200)

(0834 09341000)

C5 (0660 08801068)

(0500 06940800)

(0914 12001534)

(0934 11001500)

(1000 10001000)

(1400 18342300)

(1200 17002200)

(1200 16002100)

C6 (0868 10001000)

(0702 09341100)

(0734 08681000)

(0680 07681034)

(0506 06800902)

(1000 10001000)

(1000 11001300)

(0880 10001134)

C7 (0760 08000968)

(0734 09681200)

(1000 10001100)

(0868 10001100)

(0460 06020868)

(0834 09341000)

(1000 10001000)

(1100 12001400)

C8 (0648 08340934)

(0700 08021100)

(0900 10681300)

(1000 11001300)

(0494 06680868)

(1000 11341300)

(0814 09000934)

(1000 10001000)

Table 7 Fuzzy criteria weights 1113957wcriteria (1113957w1 1113957w2 1113957wn) determined with F-AHP

Criteria Fuzzy weightsC1 (0116 0168 0242)C2 (0094 0141 0214)C3 (0079 0112 0164)C4 (0074 0107 0152)C5 (0093 0144 0212)C6 (0079 0109 0149)C7 (0082 0110 0152)C8 (0079 0110 0153)

Table 8 5 DMsrsquo evaluation scores of the influenza intervention alternatives with respect to each criterion

C1 C2 C3 C4 C5 C6 C7 C8

A1

MG G F G VP VG VP MGG G MG MG MP VG G GVG VG F G MP F G GMG MP VG F G MP VG GF MG MG G MP G G G

A2

VG G VG VG VG VG VG GG G VG VG G VG VG GMP F F MG G MG VG GG P P G F MP G GG G G MG VG F MG MG

A3

MP VG VG P MP F VP FF G G F MP VP VP MPVG VG VG G MP P VP PG VG MP F P F F VPVP P MP MP VP P P VP


advantage over A3 Also A2 is better ranked than A3 in termsof Si andRi values as shown in Table 11 so there is acceptablestability in decision-making

Although based onQi values A1 is better ranked than A2A1 does not have comparative advantage over A2 socompromise solutions A1 and A2 are same and they bothhave comparative advantage over A3 So based on theseevaluations and calculations mass vaccination strategy andantiviral treatment and isolation of infected individualsstrategy are found to be the best intervention strategies withno reasonable difference and exclusion of people from highrisk areas strategy is determined to be worse than both ofthese strategies

4 Conclusions

In this study the results of a multicriteria decision analysisfor effective management of a health issue-influenza arepresented More specifically in this research an integratedfuzzy AHP-VIKOR method is implemented to evaluateinfluenza intervention strategies At present there does notappear to be a MCDA in the literature for the evaluation ofinfluenza intervention strategies Expert opinion for thedevelopment of pairwise comparisonmatrices of criteria andevaluation of alternatives was needed in the fuzzy AHP-VIKOR method so a professor of infectious diseases andclinical microbiology an internal medicine physician anENT physician a family physician and a cardiologist in

Turkey acted as DMs in the study Based on their evaluationmass vaccination and antiviral treatment and isolation ofinfected individuals are determined as the best interventionstrategies with no comparative advantage and exclusion ofpeople from high risk areas (mass measurements to reducethe contact rate ie school closures and closure of publicplaces) is determined to be the worst alternative among theevaluated

For future research the proposed fuzzy AHP-VIKORmethod and determined evaluation criteria can be adoptedand utilized by physicians for the evaluation and ranking ofintervention strategies for similar diseases Also outer de-pendence innerdependence and feedback relationshipsbetween evaluation criteria can be investigated with thefuzzy analytic network process (F-ANP) and F-ANP can beintegrated with F-VIKOR for healthcare-related evaluationand ranking problems such as drug selection and treatmentselection

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Table 9 Fuzzy evaluation matrix ( 1113957D) for the alternatives and fuzzy best values (FBV) and fuzzy worst values (FWV)

C1 C2 C3 C4 C5 C6 C7 C8

A1 (5800 76009000)

(5800 76008800)

(5000 68008400)

(5800 78009200)

(2000 36005200)

(5800 74008400)

(6000 74008200)

(6600 86009800)

A2 (6200 80009000)

(4800 66008000)

(5600 70008000)

(7000 86009600)

(7000 86009400)

(5400 70008200)

(7800 92009800)

(6600 86009800)

A3 (4000 54006600)

(6800 80008600)

(5400 70008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

FBV (6200 80009000)

(6800 80008800)

(5600 70008400)

(7000 86009600)

(7000 86009400)

(5800 74008400)

(7800 92009800)

(6600 86009800)

FWV (4000 54006600)

(4800 66008000)

(5000 68008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

Table 10 1113957Si 1113957Ri 1113957Slowast 1113957S


minus values

1113957Si1113957Ri

1113957Qi

A1 (minus 1744 0333 4200) (0019 0112 1691) (minus 1133 0150 1025)A2 (minus 1841 0150 3379) (minus 0032 0141 1691) (minus 1050 0256 1050)A3 (minus 1576 0747 4404) (0047 0168 1724) (minus 1164 1000 1000)1113957Slowast

(minus 841 0150 3379) 1113957Rlowast

(minus 0032 0112 1691)1113957S

minus (minus 1576 0747 4404) 1113957R

minus (0047 0168 1724)

Table 11 Fuzzy AHP-VIKOR results for influenza intervention strategies

Si Rank Ri Rank Qi Rank

A1 0632 2 0360 1 0085 1A2 0356 1 0370 2 0171 2A3 0969 3 0407 3 0639 3


Acknowledgments

is research was supported by Kadir Has UniversityIstanbul Turkey (2017-BAP-16) e author would like toacknowledge and thank Prof Dr Onder Ergonul MD MPH(Infectious Diseases) Murat Gorgulu MD (internal medi-cine) Gani Atilla Sengor MD (ENT) Selccediluk Uyanık MD(family physician) and Zeki Ozyedek MD (cardiologist) fortheir collaboration in this research

References

[1] S Cauchemez M D Van Kerkhove B N Archer et alldquoSchool closures during the 2009 influenza pandemic na-tional and local experiencesrdquo BMC Infectious Diseases vol 14no 1 p 207 2014

[2] J Kelso N Halder and G Milne ldquoVaccination strategies forfuture influenza pandemics a severity-based cost effectivenessanalysis (provisional abstract)rdquo BMC Infectious Diseasesvol 13 no 1 p 81 2013

[3] European Center for Disease Prevention and Control ldquoe2009 A(H1N1) pandemic in Europe reproductionrdquo SpecialReport European Center for Disease Prevention and ControlStocholm Sweden 2010

[4] J Mereckiene S Cotter J T Weber et al ldquoInfluenzaA(H1N1)pdm09 vaccination policies and coverage inEuroperdquo Eurosurveillance vol 17 no 4 Article ID 200642012

[5] F Samanlioglu and A H Bilge ldquoAn overview of the 2009A(H1N1) pandemic in Europe efficiency of the vaccinationand healthcare strategiesrdquo Journal of Healthcare Engineeringvol 2016 Article ID 5965836 13 pages 2016

[6] B Freiesleben de Blasio B G Iversen and G Tomba ldquoEffectof vaccines and antivirals during the major 2009 A(H1N1)pandemic wave in Norwaymdashand the influence of vaccinationtimingrdquo PLoS One vol 7 no 1 Article ID e30018 2012

[7] K Waalen A Kilander S G Dudman G H Krogh T Auneand O Hungnes ldquoHigh prevalence of antibodies to the 2009pandemic influenza A(H1N1) virus in the Norwegian pop-ulation following a major epidemic and a large vaccinationcampaign in autumn 2009rdquo Eurosurveillance vol 15 no 31Article ID 19633 2010

[8] S Merler M Ajelli A Pugliese and N M Ferguson ldquoDe-terminants of the spatiotemporal dynamics of the 2009 H1N1pandemic in Europe implications for real-timemodellingrdquo PLoSComputational Biology vol 7 no 9 Article ID e1002205 2011

[9] HWilking S Buda E von der Lippe et al ldquoMortality of 2009pandemic influenza A (H1N1) in Germanyrdquo Eurosurveillancevol 15 no 49 Article ID 19741 2010

[10] 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

[11] 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

[12] 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 p 897 2013

[13] S Pooripussarakul A Riewpaiboon D Bishai C Muangchanaand S Tantivess ldquoWhat criteria do decision makers in ailand

use to set priorities for vaccine introductionrdquo BMC PublicHealth vol 16 no 1 p 684 2016

[14] L A Zadeh ldquoFuzzy logic neural networks and soft computingrdquoCommunications of the ACM vol 37 no 3 pp 77ndash84 1994

[15] T L Saatye Analytic Hierarchy Process McGraw-Hill IncNew York NY USA 1980

[16] S F Weber ldquoA modified analytic hierarchy process for au-tomated manufacturing decisionsrdquo Interfaces vol 23 no 4pp 75ndash84 1993

[17] M Yurdakul ldquoAHP as a strategic decision-making tool tojustify machine tool selectionrdquo Journal of Materials ProcessingTechnology vol 146 no 3 pp 365ndash376 2004

[18] Z Ayag ldquoA hybrid approach to machine-tool selectionthrough AHP and simulationrdquo International Journal ofProduction Research vol 45 no 9 pp 2029ndash2050 2007

[19] K-T Cho and S-M Kim ldquoSelecting medical devices andmaterials for development in Korea the analytic hierarchyprocess approachrdquo e International Journal of HealthPlanning and Management vol 18 no 2 pp 161ndash174 2003

[20] S Opricovic Multicriteria optimization of civil engineeringsystems PhD thesis Faculty of Civil Engineering BelgradeSerbia 1998

[21] G-H Tzeng M-H Teng J-J Chen and S OpricovicldquoMulticriteria selection for a restaurant location in TaipeirdquoInternational Journal of Hospitality Management vol 21no 2 pp 171ndash187 2002

[22] S Opricovic and G-H Tzeng ldquoCompromise solution byMCDM methods a comparative analysis of VIKOR andTOPSISrdquo European Journal of Operational Research vol 156no 2 pp 445ndash455 2004

[23] G-H Tzeng C-W Lin and S Opricovic ldquoMulti-criteriaanalysis of alternative-fuel buses for public transportationrdquoEnergy Policy vol 33 no 11 pp 1373ndash1383 2005

[24] S Opricovic and G-H Tzeng ldquoExtended VIKOR method incomparison with outranking methodsrdquo European Journal ofOperational Research vol 178 no 2 pp 514ndash529 2007

[25] S Opricovic ldquoFuzzy VIKOR with an application to waterresources planningrdquo Expert Systems with Applications vol 38no 10 pp 12983ndash12990 2011

[26] S-P Wan Q-Y Wang and J-Y Dong ldquoe extendedVIKOR method for multi-attribute group decision makingwith triangular intuitionistic fuzzy numbersrdquo Knowledge-Based Systems vol 52 pp 65ndash77 2013

[27] Y Ju and A Wang ldquoExtension of VIKOR method for multi-criteria group decision making problem with linguistic in-formationrdquo Applied Mathematical Modelling vol 37 no 5pp 3112ndash3125 2013

[28] H-C Liu J-X You X-J Fan and Y-Z Chen ldquoSite selection inwaste management by the VIKOR method using linguistic as-sessmentrdquo Applied Soft Computing vol 21 pp 453ndash461 2014

[29] J Qin X Liu and W Pedrycz ldquoAn extended VIKOR methodbased on prospect theory for multiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowl-edge-Based Systems vol 86 pp 116ndash130 2015

[30] I Yazici and C Kahraman ldquoVIKOR method using intervaltype two fuzzy setsrdquo Journal of Intelligent amp Fuzzy Systemsvol 29 no 1 pp 411ndash421 2015

[31] S Narayanamoorthy and S Geetha ldquoIntuitionistic hesitantfuzzy VIKOR method for multi-criteria group decisionmakingrdquo International Journal of Pure and Applied Mathe-matics vol 113 no 9 pp 102ndash112 2017

[32] Z Ayag ldquoA fuzzy AHP-based simulation approach to conceptevaluation in a NPD environmentrdquo IIE Transactions vol 37no 9 pp 827ndash842 2005


[33] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[34] O Duran and J Aguilo ldquoComputer-aided machine-tool se-lection based on a fuzzy-AHP approachrdquo Expert Systems withApplications vol 34 no 3 pp 1787ndash1794 2008

[35] P Srichetta and W urachon ldquoApplying fuzzy analytichierarchy process to evaluate and select product of notebookcomputersrdquo International Journal of Modeling and Optimi-zation vol 2 no 2 pp 168ndash173 2012

[36] 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 2014

[37] G Kabir and R S Sumi ldquoPower substation location selectionusing fuzzy analytic hierarchy process and PROMETHEE a casestudy from Bangladeshrdquo Energy vol 72 pp 717ndash730 2014

[38] 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

[39] G Sakthivel M Ilangkumaran G Nagarajan andP Shanmugam ldquoSelection of best biodiesel blend for ICengines an integrated approach with FAHP-TOPSIS andFAHP-VIKORrdquo International Journal of Oil Gas and CoalTechnology vol 6 no 5 p 581 2013

[40] Y Kim and E-S Chung ldquoFuzzy VIKOR approach forassessing the vulnerability of the water supply to climatechange and variability in South Koreardquo Applied MathematicalModelling vol 37 no 22 pp 9419ndash9430 2013

[41] A Jahan F Mustapha M Y Ismail S M Sapuan andM Bahraminasab ldquoA comprehensive VIKOR method formaterial selectionrdquo Materials amp Design vol 32 no 3pp 1215ndash1221 2011

[42] Z-X Su ldquoA hybrid fuzzy approach to fuzzy multi-attributegroup decision-makingrdquo International Journal of InformationTechnology amp Decision Making vol 10 no 4 pp 695ndash7112011

[43] T-H Chang ldquoFuzzy VIKOR method a case study of thehospital service evaluation in Taiwanrdquo Information Sciencesvol 271 pp 196ndash212 2014

[44] 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

[45] S Musani and A A Jemain ldquoRanking schoolsrsquo academicperformance using a fuzzy VIKORrdquo Journal of PhysicsConference Series vol 622 Article ID 012036 2015

[46] A Awasthi and G Kannan ldquoGreen supplier developmentprogram selection using NGT and VIKOR under fuzzy en-vironmentrdquo Computers amp Industrial Engineering vol 91pp 100ndash108 2016

[47] M Yazdani and F R Graeml ldquoVIKOR and its applicationsrdquoInternational Journal of Strategic Decision Sciences vol 5no 2 pp 56ndash83 2014

[48] M Gul E Celik N Aydin A Taskin Gumus andA F Guneri ldquoA state of the art literature review of VIKORand its fuzzy extensions on applicationsrdquo Applied SoftComputing vol 46 pp 60ndash89 2016

[49] A Shahrasbi M Shamizanjani M H Alavidoost andB Akhgar ldquoAn aggregated fuzzy model for the selection of amanaged security service providerrdquo International Journal ofInformation Technology amp Decision Making vol 16 no 3pp 625ndash684 2017

[50] Y Ali M Razi F De Felice M Sabir and A Petrillo ldquoAVIKOR based approach for assessing the social environ-mental and economic effects of ldquosmogrdquo on human healthrdquoScience of the Total Environment vol 650 pp 2897ndash29052019

[51] Y Ali M Asees Awan M Bilal J Khan A Petrillo and A AliKhan ldquoRisk assessment of China-Pakistan fiber optic project(CPFOP) in the light of multi-criteria decision making(MCDM)rdquo Advanced Engineering Informatics vol 40pp 36ndash45 2019

[52] T Kaya and C Kahraman ldquoMulticriteria renewable energyplanning using an integrated fuzzy VIKOR amp AHP meth-odology the case of Istanbulrdquo Energy vol 35 no 6pp 2517ndash2527 2010

[53] M Ilangkumaran V Sasirekha L Anojkumar andM B Raja ldquoMachine tool selection using AHP and VIKORmethodologies under fuzzy environmentrdquo InternationalJournal of Modelling in Operations Management vol 2 no 4pp 409ndash436 2012

[54] H Dincer and U Hacioglu ldquoPerformance evaluation withfuzzy VIKOR and AHP method based on customer satis-faction in Turkish banking sectorrdquo Kybernetes vol 42 no 7pp 1072ndash1085 2013

[55] A S Ghadikolaei S K Esbouei and J AntuchevicieneldquoApplying fuzzy MCDM for financial performance evaluationof Iranian companiesrdquo Technological and Economic Devel-opment of Economy vol 20 no 2 pp 274ndash291 2014

[56] K Rezaie S S Ramiyani S Nazari-Shirkouhi andA Badizadeh ldquoEvaluating performance of Iranian cementfirms using an integrated fuzzy AHP-VIKOR methodrdquo Ap-plied Mathematical Modelling vol 38 no 21-22 pp 5033ndash5046 2014

[57] 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

[58] S Aydin and C Kahraman ldquoVehicle selection for publictransportation using an integrated multi criteria decisionmaking approach a case of Ankarardquo Journal of Intelligent ampFuzzy Systems vol 26 no 5 pp 2467ndash2481 2014

[59] V A Bhosale and R Kant ldquoSelection of best knowledge flowpracticing organisation using hybrid fuzzy AHP-VIKORmethodrdquo International Journal of Decision Sciences Risk andManagement vol 5 no 3 pp 234ndash262 2014

[60] A P S Arunachalam S Idapalapati and S Subbiah ldquoMulti-criteria decision making techniques for compliant polishingtool selectionrdquo e International Journal of AdvancedManufacturing Technology vol 79 no 1ndash4 pp 519ndash530 2015

[61] G J Klir and B Yuan Fuzzy Sets and Fuzzy Logic eory andApplications Springer New York NY USA 1995

[62] F A Lootsma Fuzzy Logic for Planning and Decision MakingApplied Optimization Springer New York NY USA 1997

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

[64] M Asees Awan and Y Ali ldquoSustainable modeling in reverselogistics strategies using fuzzy MCDM case of China PakistanEconomic CorridorrdquoManagement of Environmental QualityAn International Journal vol 30 no 5 pp 1132ndash1151 2019

[65] L Y Chen and T-C Wang ldquoOptimizing partnersrsquo choice inISIT outsourcing projects the strategic decision of fuzzyVIKORrdquo International Journal of Production Economicsvol 120 no 1 pp 233ndash242 2009


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

decisions related to intervention strategies during an in-fluenza pandemic especially for transparency and ac-countability of the decision-making process Evaluation ofintervention strategies is a significant MCDM problem thatrequires expertise and competency since there are variouspotentially conflicting criteria to take into consideration Inthe literature there are a few studies that utilize MCDMmethods for evaluation of intervention strategies Shin et al[10] used AHP to evaluate the expanded Korean immuni-zation programs and assess two policies weather privateclinics and hospitals or public health centers should offer freevaccination services to children Mourits et al [11] applied theEVAMIX (evaluations with mixed data) MCDM method torank alternative strategies to control classical swine feverepidemics in EU Aenishaenslin et al [12] implementedD-Sight which uses PROMETHEE methods (PreferenceRanking Organization Method for Enrichment Evaluations)and gives access to the GAIA (Geometrical Analysis forInteractive Aid) to assess various prevention and controlstrategies for the Lyme disease in Quebec Canada eydeveloped two MCDM models one for surveillance in-terventions and one for control interventions and conductedthe analysis under a disease emergence and an epidemicscenario Pooripussarakul et al [13] implemented best-worstscaling to assess and rank-order vaccines for introduction intothe expanded program on immunization in ailand

In this study various influenza intervention strategiesare evaluated taking into consideration potentially con-flicting criteria by five physicians with different expertisesacting as consultants and decision makers (DMs) As theMCDMmethod and integrated method fuzzy AHP-VIKORis implemented to evaluate and rank the strategies In fuzzyAHP-VIKOR F-AHP is implemented to find the fuzzycriteria weights and F-VIKOR is utilized to rank alternativesusing these weights Here an integrated method is used tohave both methodsrsquo advantages F-VIKOR is easy to use forMCDM problems with especially conflicting criteria how-ever it does not include guidelines for determining theweights of criteria and with F-AHP through pairwisecomparisons reliable fuzzy weights can be obtained Withthe integrated fuzzy AHP-VIKOR intervention strategiesare ranked without too many repetitive pairwise compari-sons and complicated calculations

e fuzzy set theory is a mathematical theory designed tomodel the vagueness or imprecision of human cognitiveprocesses It is a theory of classes with unsharp boundariesand any crisp theory can be fuzzified by generalizing theconcept of a set within that theory to the concept of a fuzzyset [14] Fuzzy extensions of AHP (F-AHP) and VIKOR (F-VIKOR) are used to capture the uncertainty and vaguenesson judgments of DMs

In AHP [15] alternatives are evaluated based on variouscriteria in a hierarchical and multilevel structure and thenalternatives are ranked based on a calculated total weightedscore AHP is used widely in real-life applications ie fordecisions related to machine shops [16] for evaluation ofmachine tools [17 18] and for evaluation of medical devicesand materials [19] e VIKOR method was introducedmainly for MCDM problems with competing or

noncommensurable criteria In VIKOR compromise rankingis performed and alternatives are compared according to thecloseness to the ideal solution [20ndash23] To reflect the un-certainty and vagueness on judgments of DMs their fuzzyextensions F-AHP and F-VIKOR have been developedWithF-VIKOR an accepted compromise solution is obtained witha maximum group utility of the majority and a minimum ofindividual regret of the opponent [22 24] In the literaturedifferent versions of F-VIKOR exist such as F-VIKOR withTriangular fuzzy numbers [24 25] triangular intuitionisticfuzzy numbers [26] 2-tuple group decision-making linguisticmodel [27] an attitudinal-based interval 2-tuple linguisticmodel [28] type-2 fuzzy model [29 30] and an intuitionistichesitant model using entropy weights [31] Several real-lifeapplications of F-AHP F-VIKOR and fuzzy AHP-VIKORare given in Table 1

At present there does not appear to be a research paperin the literature that focuses on evaluation and ranking ofinfluenza intervention strategies Moreover fuzzy AHP-VIKOR has never been used in the evaluation of in-tervention strategies for a pandemic In the next sectionsfuzzy AHP-VIKOR steps and a case study are presented

2 Proposed Fuzzy AHP-VIKOR Approach

21 Definitions In fuzzy set theory there are classes withunsharp boundaries [61 62] Any crisp theory can be fuz-zified using the concept of a fuzzy set [14] In the proposedfuzzy AHP-VIKOR triangular fuzzy numbers (TFNs) areused due to its simplicity A fuzzy number is a special fuzzyset F (x μF(x)) x isin R1113864 1113865 Here R minus infinlt xlt +infin andμF(x) is from R to [0 1] A TFN denoted as 1113957M (l m u)where llemle u has the membership function

μF(x)

0 xlt l

x minus l

m minus l llexlem

u minus x

u minus m mlexle u

0 xgt u

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

Basic operations between two positive TFNs 1113957A (l1

m1 u1) 1113957B (l2 m2 u2) l1 lem1 le u1 l2 lem2 le u2 and acrisp number C(Cge 0) are explained as follows

1113957A + 1113957B l1 + l2 m1 + m2 u1 + u2( 1113857

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

1113957A minus 1113957B l1 minus u2 m1 minus m2 u1 minus l2( 1113857

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

1113957Alowast 1113957B l1 lowast l2 m1 lowastm2 u1 lowastu2( 1113857

1113957AlowastC l1 lowastC m1 lowastC u1 lowastC( 1113857

1113957A

1113957B

l1

u2m1

m2u1

l21113888 1113889


1113957A

1113957B min

l1

l2

l1

u2u1

l2u1

u21113888 1113889

m1

m2 max

l1

l2

l1

u2u1

l2u1

u21113888 11138891113888 1113889


1113957A

C

l1

Cm1

Cu1

C1113888 1113889 for Cgt 0

1113957Aminus 1

1u1

1

m11l1

1113888 1113889



(2)


crisp(1113957A) 4m1 + l1 + u1( 1113857

6 (3)





(1K)(1113957x1ij(+)1113957x2


ij (aKij bK

ij cKij)


Step 2 1113957X






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with ele-


1113957S






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦














XwTcr λmaxw

Tcr (4)


CI λmax minus n

n minus 1 (5)


CR CIRI

(6)







ij (aKij bK

ij ckij) is the








⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

where





1113957flowastj max

i1113957rij forallj

1113957fminus

j mini



1113957Si 1113944n

j1



minus

j1113872 1113873 foralli

1113957Ri maxj



minus

j


(8)



minus values as

1113957Slowast

mini

1113957Si

1113957Sminus

maxi

1113957Si

1113957Rlowast

mini

1113957Ri

1113957Rminus

maxi

1113957Ri

(9)


1113957Qi ]1113957Si minus 1113957S

lowast

1113957Sminus



1113957Rminus















3 Case Study





minus












C1 C2 C3 C4 C5 C6 C7 C8

C1


C2


C3


C4


C5


C6


C7

E EE SSE EE VSE E

C8

EEEEE






C1 C2 C3 C4 C5 C6 C7 C8

C1 (1000 10001000)

(1700 21002500)

(0900 12001500)

(1334 18002200)

(1280 16002034)

(1000 10001200)

(1134 14001600)

(1100 13001700)

C2 (0478 05400634)

(1000 10001000)

(1100 16002100)

(1100 14001900)

(1400 17002200)

(0934 11001500)

(0900 11341500)

(0934 13001600)

C3 (0480 05680734)

(0480 06360934)

(1000 10001000)

(1000 13001700)

(0814 10341334)

(1000 12001500)

(0934 10001000)

(0880 11001334)

C4 (0520 06000836)

(0548 07680934)

(0634 08021000)

(1000 10001000)

(0702 09341100)

(1034 14001700)

(0934 10001200)

(0834 09341000)

C5 (0660 08801068)

(0500 06940800)

(0914 12001534)

(0934 11001500)

(1000 10001000)

(1400 18342300)

(1200 17002200)

(1200 16002100)

C6 (0868 10001000)

(0702 09341100)

(0734 08681000)

(0680 07681034)

(0506 06800902)

(1000 10001000)

(1000 11001300)

(0880 10001134)

C7 (0760 08000968)

(0734 09681200)

(1000 10001100)

(0868 10001100)

(0460 06020868)

(0834 09341000)

(1000 10001000)

(1100 12001400)

C8 (0648 08340934)

(0700 08021100)

(0900 10681300)

(1000 11001300)

(0494 06680868)

(1000 11341300)

(0814 09000934)

(1000 10001000)




C1 C2 C3 C4 C5 C6 C7 C8

A1


A2


A3





4 Conclusions




Data Availability





C1 C2 C3 C4 C5 C6 C7 C8

A1 (5800 76009000)

(5800 76008800)

(5000 68008400)

(5800 78009200)

(2000 36005200)

(5800 74008400)

(6000 74008200)

(6600 86009800)

A2 (6200 80009000)

(4800 66008000)

(5600 70008000)

(7000 86009600)

(7000 86009400)

(5400 70008200)

(7800 92009800)

(6600 86009800)

A3 (4000 54006600)

(6800 80008600)

(5400 70008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

FBV (6200 80009000)

(6800 80008800)

(5600 70008400)

(7000 86009600)

(7000 86009400)

(5800 74008400)

(7800 92009800)

(6600 86009800)

FWV (4000 54006600)

(4800 66008000)

(5000 68008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)



minus values

1113957Si1113957Ri

1113957Qi


(minus 841 0150 3379) 1113957Rlowast

(minus 0032 0112 1691)1113957S

minus (minus 1576 0747 4404) 1113957R

minus (0047 0168 1724)



A1 0632 2 0360 1 0085 1A2 0356 1 0370 2 0171 2A3 0969 3 0407 3 0639 3


Acknowledgments


References







































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


1113957A

1113957B min

l1

l2

l1

u2u1

l2u1

u21113888 1113889

m1

m2 max

l1

l2

l1

u2u1

l2u1

u21113888 11138891113888 1113889


1113957A

C

l1

Cm1

Cu1

C1113888 1113889 for Cgt 0

1113957Aminus 1

1u1

1

m11l1

1113888 1113889



(2)


crisp(1113957A) 4m1 + l1 + u1( 1113857

6 (3)





(1K)(1113957x1ij(+)1113957x2


ij (aKij bK

ij cKij)


Step 2 1113957X






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with ele-


1113957S






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦














XwTcr λmaxw

Tcr (4)


CI λmax minus n

n minus 1 (5)


CR CIRI

(6)







ij (aKij bK

ij ckij) is the








⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

where





1113957flowastj max

i1113957rij forallj

1113957fminus

j mini



1113957Si 1113944n

j1



minus

j1113872 1113873 foralli

1113957Ri maxj



minus

j


(8)



minus values as

1113957Slowast

mini

1113957Si

1113957Sminus

maxi

1113957Si

1113957Rlowast

mini

1113957Ri

1113957Rminus

maxi

1113957Ri

(9)


1113957Qi ]1113957Si minus 1113957S

lowast

1113957Sminus



1113957Rminus















3 Case Study





minus












C1 C2 C3 C4 C5 C6 C7 C8

C1


C2


C3


C4


C5


C6


C7

E EE SSE EE VSE E

C8

EEEEE






C1 C2 C3 C4 C5 C6 C7 C8

C1 (1000 10001000)

(1700 21002500)

(0900 12001500)

(1334 18002200)

(1280 16002034)

(1000 10001200)

(1134 14001600)

(1100 13001700)

C2 (0478 05400634)

(1000 10001000)

(1100 16002100)

(1100 14001900)

(1400 17002200)

(0934 11001500)

(0900 11341500)

(0934 13001600)

C3 (0480 05680734)

(0480 06360934)

(1000 10001000)

(1000 13001700)

(0814 10341334)

(1000 12001500)

(0934 10001000)

(0880 11001334)

C4 (0520 06000836)

(0548 07680934)

(0634 08021000)

(1000 10001000)

(0702 09341100)

(1034 14001700)

(0934 10001200)

(0834 09341000)

C5 (0660 08801068)

(0500 06940800)

(0914 12001534)

(0934 11001500)

(1000 10001000)

(1400 18342300)

(1200 17002200)

(1200 16002100)

C6 (0868 10001000)

(0702 09341100)

(0734 08681000)

(0680 07681034)

(0506 06800902)

(1000 10001000)

(1000 11001300)

(0880 10001134)

C7 (0760 08000968)

(0734 09681200)

(1000 10001100)

(0868 10001100)

(0460 06020868)

(0834 09341000)

(1000 10001000)

(1100 12001400)

C8 (0648 08340934)

(0700 08021100)

(0900 10681300)

(1000 11001300)

(0494 06680868)

(1000 11341300)

(0814 09000934)

(1000 10001000)




C1 C2 C3 C4 C5 C6 C7 C8

A1


A2


A3





4 Conclusions




Data Availability





C1 C2 C3 C4 C5 C6 C7 C8

A1 (5800 76009000)

(5800 76008800)

(5000 68008400)

(5800 78009200)

(2000 36005200)

(5800 74008400)

(6000 74008200)

(6600 86009800)

A2 (6200 80009000)

(4800 66008000)

(5600 70008000)

(7000 86009600)

(7000 86009400)

(5400 70008200)

(7800 92009800)

(6600 86009800)

A3 (4000 54006600)

(6800 80008600)

(5400 70008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

FBV (6200 80009000)

(6800 80008800)

(5600 70008400)

(7000 86009600)

(7000 86009400)

(5800 74008400)

(7800 92009800)

(6600 86009800)

FWV (4000 54006600)

(4800 66008000)

(5000 68008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)



minus values

1113957Si1113957Ri

1113957Qi


(minus 841 0150 3379) 1113957Rlowast

(minus 0032 0112 1691)1113957S

minus (minus 1576 0747 4404) 1113957R

minus (0047 0168 1724)



A1 0632 2 0360 1 0085 1A2 0356 1 0370 2 0171 2A3 0969 3 0407 3 0639 3


Acknowledgments


References







































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




XwTcr λmaxw

Tcr (4)


CI λmax minus n

n minus 1 (5)


CR CIRI

(6)







ij (aKij bK

ij ckij) is the








⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

where





1113957flowastj max

i1113957rij forallj

1113957fminus

j mini



1113957Si 1113944n

j1



minus

j1113872 1113873 foralli

1113957Ri maxj



minus

j


(8)



minus values as

1113957Slowast

mini

1113957Si

1113957Sminus

maxi

1113957Si

1113957Rlowast

mini

1113957Ri

1113957Rminus

maxi

1113957Ri

(9)


1113957Qi ]1113957Si minus 1113957S

lowast

1113957Sminus



1113957Rminus















3 Case Study





minus












C1 C2 C3 C4 C5 C6 C7 C8

C1


C2


C3


C4


C5


C6


C7

E EE SSE EE VSE E

C8

EEEEE






C1 C2 C3 C4 C5 C6 C7 C8

C1 (1000 10001000)

(1700 21002500)

(0900 12001500)

(1334 18002200)

(1280 16002034)

(1000 10001200)

(1134 14001600)

(1100 13001700)

C2 (0478 05400634)

(1000 10001000)

(1100 16002100)

(1100 14001900)

(1400 17002200)

(0934 11001500)

(0900 11341500)

(0934 13001600)

C3 (0480 05680734)

(0480 06360934)

(1000 10001000)

(1000 13001700)

(0814 10341334)

(1000 12001500)

(0934 10001000)

(0880 11001334)

C4 (0520 06000836)

(0548 07680934)

(0634 08021000)

(1000 10001000)

(0702 09341100)

(1034 14001700)

(0934 10001200)

(0834 09341000)

C5 (0660 08801068)

(0500 06940800)

(0914 12001534)

(0934 11001500)

(1000 10001000)

(1400 18342300)

(1200 17002200)

(1200 16002100)

C6 (0868 10001000)

(0702 09341100)

(0734 08681000)

(0680 07681034)

(0506 06800902)

(1000 10001000)

(1000 11001300)

(0880 10001134)

C7 (0760 08000968)

(0734 09681200)

(1000 10001100)

(0868 10001100)

(0460 06020868)

(0834 09341000)

(1000 10001000)

(1100 12001400)

C8 (0648 08340934)

(0700 08021100)

(0900 10681300)

(1000 11001300)

(0494 06680868)

(1000 11341300)

(0814 09000934)

(1000 10001000)




C1 C2 C3 C4 C5 C6 C7 C8

A1


A2


A3





4 Conclusions




Data Availability





C1 C2 C3 C4 C5 C6 C7 C8

A1 (5800 76009000)

(5800 76008800)

(5000 68008400)

(5800 78009200)

(2000 36005200)

(5800 74008400)

(6000 74008200)

(6600 86009800)

A2 (6200 80009000)

(4800 66008000)

(5600 70008000)

(7000 86009600)

(7000 86009400)

(5400 70008200)

(7800 92009800)

(6600 86009800)

A3 (4000 54006600)

(6800 80008600)

(5400 70008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

FBV (6200 80009000)

(6800 80008800)

(5600 70008400)

(7000 86009600)

(7000 86009400)

(5800 74008400)

(7800 92009800)

(6600 86009800)

FWV (4000 54006600)

(4800 66008000)

(5000 68008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)



minus values

1113957Si1113957Ri

1113957Qi


(minus 841 0150 3379) 1113957Rlowast

(minus 0032 0112 1691)1113957S

minus (minus 1576 0747 4404) 1113957R

minus (0047 0168 1724)



A1 0632 2 0360 1 0085 1A2 0356 1 0370 2 0171 2A3 0969 3 0407 3 0639 3


Acknowledgments


References







































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









3 Case Study





minus












C1 C2 C3 C4 C5 C6 C7 C8

C1


C2


C3


C4


C5


C6


C7

E EE SSE EE VSE E

C8

EEEEE






C1 C2 C3 C4 C5 C6 C7 C8

C1 (1000 10001000)

(1700 21002500)

(0900 12001500)

(1334 18002200)

(1280 16002034)

(1000 10001200)

(1134 14001600)

(1100 13001700)

C2 (0478 05400634)

(1000 10001000)

(1100 16002100)

(1100 14001900)

(1400 17002200)

(0934 11001500)

(0900 11341500)

(0934 13001600)

C3 (0480 05680734)

(0480 06360934)

(1000 10001000)

(1000 13001700)

(0814 10341334)

(1000 12001500)

(0934 10001000)

(0880 11001334)

C4 (0520 06000836)

(0548 07680934)

(0634 08021000)

(1000 10001000)

(0702 09341100)

(1034 14001700)

(0934 10001200)

(0834 09341000)

C5 (0660 08801068)

(0500 06940800)

(0914 12001534)

(0934 11001500)

(1000 10001000)

(1400 18342300)

(1200 17002200)

(1200 16002100)

C6 (0868 10001000)

(0702 09341100)

(0734 08681000)

(0680 07681034)

(0506 06800902)

(1000 10001000)

(1000 11001300)

(0880 10001134)

C7 (0760 08000968)

(0734 09681200)

(1000 10001100)

(0868 10001100)

(0460 06020868)

(0834 09341000)

(1000 10001000)

(1100 12001400)

C8 (0648 08340934)

(0700 08021100)

(0900 10681300)

(1000 11001300)

(0494 06680868)

(1000 11341300)

(0814 09000934)

(1000 10001000)




C1 C2 C3 C4 C5 C6 C7 C8

A1


A2


A3





4 Conclusions




Data Availability





C1 C2 C3 C4 C5 C6 C7 C8

A1 (5800 76009000)

(5800 76008800)

(5000 68008400)

(5800 78009200)

(2000 36005200)

(5800 74008400)

(6000 74008200)

(6600 86009800)

A2 (6200 80009000)

(4800 66008000)

(5600 70008000)

(7000 86009600)

(7000 86009400)

(5400 70008200)

(7800 92009800)

(6600 86009800)

A3 (4000 54006600)

(6800 80008600)

(5400 70008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

FBV (6200 80009000)

(6800 80008800)

(5600 70008400)

(7000 86009600)

(7000 86009400)

(5800 74008400)

(7800 92009800)

(6600 86009800)

FWV (4000 54006600)

(4800 66008000)

(5000 68008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)



minus values

1113957Si1113957Ri

1113957Qi


(minus 841 0150 3379) 1113957Rlowast

(minus 0032 0112 1691)1113957S

minus (minus 1576 0747 4404) 1113957R

minus (0047 0168 1724)



A1 0632 2 0360 1 0085 1A2 0356 1 0370 2 0171 2A3 0969 3 0407 3 0639 3


Acknowledgments


References







































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






C1 C2 C3 C4 C5 C6 C7 C8

C1 (1000 10001000)

(1700 21002500)

(0900 12001500)

(1334 18002200)

(1280 16002034)

(1000 10001200)

(1134 14001600)

(1100 13001700)

C2 (0478 05400634)

(1000 10001000)

(1100 16002100)

(1100 14001900)

(1400 17002200)

(0934 11001500)

(0900 11341500)

(0934 13001600)

C3 (0480 05680734)

(0480 06360934)

(1000 10001000)

(1000 13001700)

(0814 10341334)

(1000 12001500)

(0934 10001000)

(0880 11001334)

C4 (0520 06000836)

(0548 07680934)

(0634 08021000)

(1000 10001000)

(0702 09341100)

(1034 14001700)

(0934 10001200)

(0834 09341000)

C5 (0660 08801068)

(0500 06940800)

(0914 12001534)

(0934 11001500)

(1000 10001000)

(1400 18342300)

(1200 17002200)

(1200 16002100)

C6 (0868 10001000)

(0702 09341100)

(0734 08681000)

(0680 07681034)

(0506 06800902)

(1000 10001000)

(1000 11001300)

(0880 10001134)

C7 (0760 08000968)

(0734 09681200)

(1000 10001100)

(0868 10001100)

(0460 06020868)

(0834 09341000)

(1000 10001000)

(1100 12001400)

C8 (0648 08340934)

(0700 08021100)

(0900 10681300)

(1000 11001300)

(0494 06680868)

(1000 11341300)

(0814 09000934)

(1000 10001000)




C1 C2 C3 C4 C5 C6 C7 C8

A1


A2


A3





4 Conclusions




Data Availability





C1 C2 C3 C4 C5 C6 C7 C8

A1 (5800 76009000)

(5800 76008800)

(5000 68008400)

(5800 78009200)

(2000 36005200)

(5800 74008400)

(6000 74008200)

(6600 86009800)

A2 (6200 80009000)

(4800 66008000)

(5600 70008000)

(7000 86009600)

(7000 86009400)

(5400 70008200)

(7800 92009800)

(6600 86009800)

A3 (4000 54006600)

(6800 80008600)

(5400 70008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

FBV (6200 80009000)

(6800 80008800)

(5600 70008400)

(7000 86009600)

(7000 86009400)

(5800 74008400)

(7800 92009800)

(6600 86009800)

FWV (4000 54006600)

(4800 66008000)

(5000 68008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)



minus values

1113957Si1113957Ri

1113957Qi


(minus 841 0150 3379) 1113957Rlowast

(minus 0032 0112 1691)1113957S

minus (minus 1576 0747 4404) 1113957R

minus (0047 0168 1724)



A1 0632 2 0360 1 0085 1A2 0356 1 0370 2 0171 2A3 0969 3 0407 3 0639 3


Acknowledgments


References







































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




4 Conclusions




Data Availability





C1 C2 C3 C4 C5 C6 C7 C8

A1 (5800 76009000)

(5800 76008800)

(5000 68008400)

(5800 78009200)

(2000 36005200)

(5800 74008400)

(6000 74008200)

(6600 86009800)

A2 (6200 80009000)

(4800 66008000)

(5600 70008000)

(7000 86009600)

(7000 86009400)

(5400 70008200)

(7800 92009800)

(6600 86009800)

A3 (4000 54006600)

(6800 80008600)

(5400 70008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)

FBV (6200 80009000)

(6800 80008800)

(5600 70008400)

(7000 86009600)

(7000 86009400)

(5800 74008400)

(7800 92009800)

(6600 86009800)

FWV (4000 54006600)

(4800 66008000)

(5000 68008000)

(2800 46006400)

(0600 20003800)

(1200 24004200)

(0600 12002600)

(0800 18003400)



minus values

1113957Si1113957Ri

1113957Qi


(minus 841 0150 3379) 1113957Rlowast

(minus 0032 0112 1691)1113957S

minus (minus 1576 0747 4404) 1113957R

minus (0047 0168 1724)



A1 0632 2 0360 1 0085 1A2 0356 1 0370 2 0171 2A3 0969 3 0407 3 0639 3


Acknowledgments


References







































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Acknowledgments


References







































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


EvaluationofInfluenzaInterventionStrategiesinTurkeywith...

Documents

Transcript of EvaluationofInfluenzaInterventionStrategiesinTurkeywith...