RISK EVALUATION OF WATER CONSERVANCY IN A PUBLIC-PRIVATE PARTNERSHIP PROJECT BASED ON GREY FUZZY THEORY

Bo WANG1,2,3, Nan SHI1, Fuqiang WANG1,2,3* and Xiangtian NIE1,2,3

1 School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China.

2CollaborativeInnovationCenterofWaterResourcesEfficientUtilizationandSupportEngineering,Zhengzhou450046, China.

3 Henan Key Laboratory of Water Environment Simulation and Treatment, Zhengzhou 450046, ChinaE-mail: wangfuqiang@ncwu.edu.cn

(Received May 2018; accepted July 2018)

Key words: greyfuzzytheory,PPPproject,riskevaluation,rankcorrelationanalysis,waterconservancyproject

ABSTRACT

Inthispaper,aquantifiablemethodforriskevaluationofwaterconservancyinapublic-privatepartnership(PP)PPPprojectispresented.Firstly,accordingtothecharacteristicsofwaterconservancyPPPproject,ariskevaluationindexwasdeterminedbyDelphimethodandliteraturecollectionmethod;secondly,theweightofriskevaluationindexesweredeterminedbyrankcorrelationanalysis;thirdly,basedongreyfuzzytheory,agreyfuzzycomprehensiveevaluationmodelwasconstructed,anduncertaingreyandfuzzy contents were transformed into values that can be accurately measured, which providedabasisformanagerstomakedecisions.Finally,thegreyfuzzycomprehensiveevaluationmodelwasappliedtoFendouReservoir,awaterconservancyPPPproject,anditprovedtobereasonableandscientific.

Palabrasclave: teoríagrisdifusa,proyectoPPP,evaluaciónderiesgo,análisisdecorrelaciónderangos,proyectodeconservacióndeagua

RESUMEN

Enestetrabajosepresentaunmétododecuantificaciónparalaevaluaciónderiesgoenunproyectodecolaboraciónpúblicayprivada(PPP,porsussiglaseninglés)paraconservacióndelagua.Primero,deacuerdoconlascaracterísticasdelproyectoPPPparaconservacióndelaguasedeterminóuníndicedeevaluaciónderiesgoporelmétodoDelphiyunarevisióndeliteratura;segundo,elpesodelosíndicesdeevaluaciónderiesgoseobtuvopormediodelanálisisdecorrelaciónderangos,ytercero,seconstru-yóunmodelocomprehensivodeevaluacióngrisdifusoyloscontenidosinciertossetransformaronenvaloresmediblesconprecisiónparaservircomofundamentoalostomadoresdedecisiones.Finalmente,elmodelocomprehensivogrisdisfusoseaplicóalembalseFendou,unproyectoPPPdeconservacióndelagua,yprobóserrazonableycientífico.

Rev.Int.Contam.Ambie.35(EnvironmentalEngineeringofSustainableLandscapes)111-121,2019DOI:10.20937/RICA.2019.35.esp01.11

B. Wang et al.112

INTRODUCTION

Waterconservancyprojecthashugeinvestment,large scale, long construction period, changeableconstructionenvironmentandcomplexconstructiontechnology.To reduce the cost,makegovernmentfundsmoreefficientandgetridoftheshacklesofsocialdevelopmentcausedbytheshortageofwaterconservancy project funds, PPP (Public-Private-Partnership), a newproject financingmodel, hasbecomemore andmore popular in the field ofwaterconservancyproject inChina.Basedon theexperience of PPPmodel inAustralia, Portugal,Spainand theUK,Garvinproved thatPPPmodelhas advantages in infrastructure development inNorthAmerica(Garvin2010,Nordinetal.2017).ItisreasonableandeffectivefortheUStodeveloptransportationfacilitiesbythePPPmodelfromtheeconomic,legalandpublicpointofview(Papajohnetal.2010).AgroupresearcherillustratedthepositiveeffectofPPPmodelonthefinancialexpensesoftheprovincialgovernmentintheprojectofMetroLine4inSãoPaulo,Brazil(Brandaoetal.2012,Roslanetal.2017,Farooqietal.2017).AlmassitestedtheimportanceofAustralianPPP concession contractsetting and government guarantee mechanism to projectperformanceusingrealoptionmethod(Alietal.2013,Toumetal.2018).

PPPmodel is a new cooperationmode estab-lished by government and social capital throughfranchising. It has the characteristics of large invest-ment, long operation cycle, complex contractualrelationship and high social benefits. Shen et al.dividedrisksintointernal,externalandproject-levelrisksbyinvestigatingthemainrisksinpublicproj-ectsandthemanagementintheprojects(Shenetal.2006,Yunetal.2018).SomeresearchersfoundthatPPPprojectfinancing,especiallycapitalmarketfinancing,playsanimportantroleinthesuccessofPPPprojects(Reganetal.2011,Arshadullahetal.2017).Inanotherstudy,scientistshaveconstructeda PPP project performance index systemwith 5kinds and 48 indexes by questionnaires (Yuan etal. 2011,Usman et al. 2017).Hwang et al. col-lected the risks that arecommon toPPPprojectsinSingaporeandidentified23keyrisksbasedonquestionnaires(Hwangetal.2013,YasinandUsman2017).Agroup researcher identifiedandcounted40 risks factors and selected the key risk factorsof20waterconservancyPPPprojectsinGhanabyDelphimethod,mainlyincludingexchangeraterisk,corruptionrisk,theftrisk,politicalrisk,highcostoperation and so on (Ameyaw andChan, 2015).

Other researchers investigated and revealed therisk andPPP feasibilityof the localgovernment,aswellas therisks in thestagesofprocurement,construction, operation and transfer by question-nairesandinterviews(Shresthaetal.2017,Lietal.2018).BecauseoftheextensionofthePPPprojectinspaceandtime,andthespecializationofthewaterconservancy project, thewater conservancy PPPprojectwillhavedifferentrisksfromothermodelsintheprocessofimplementation.Findingouttherisk factorscomprehensively and reasonably anddetermining the risk evaluation index system ofwaterconservancyPPPprojectareveryimportanttothesuccessoftheproject.

Theearlyinternationalriskevaluationmethodwas single, and foreign scholars used qualitative and quantitativemethods to analyze the risk ofPPP project. For example,Kumaraswamy estab-lishedaselectionmodeloftheprojectteamintheconcession agreement to meet the requirements of the sustainable development of PPP project(KumaraswamyandZhang2001,Luetal.2018).Grimsey constructed a risk assessmentmodel ofPPPproject fromdifferentperspectivesbasedonMonteCarlomethod,andevaluatedtheeffective-ness of the model through sensitivity analysis; based onFTAandDelphimethod,Thomasproposedanevaluationframeworkforriskprobabilityandriskimpact;Shenembedded theguiding strategiesofbenefit-sharing,multi-party satisfaction and risk-sharinginthekeyissueofconcessionperiodunderPPP model with mathematical methods such as simulationandgametheory,whichhasopenedupanewideafortheresearchrelatedtoPPPprojectconcession (Grimsey and Lewis 2002, Shen etal.2007,Thomasetal.2006).Xueconstructedawell-organizedandfeasibleframeworkmodelforautomaticconcessiondecision-making,whichhasplayedasignificantroleinreducingtheriskofPPPproject(Xue2009).Iyerconstructedahierarchicalstructureand internal relationshipof risksbyus-ingInterpretativeStructuralModeling(ISM),andthendeterminedthecorrelationandinfluenceoftherisksthroughMICMACanalysis(IyerandSagheer2010).XieconstructedaPPPprojectdecisionmodelbased onmulti-party satisfaction usingBayesiannetwork,which provides effective decision sup-portinformationforstakeholdersbyusingMonteCarlo simulation method, Carbonara determined andevaluatedthefranchiseperiodofPPPprojectby constructing awin-winmodel of risk sharingbetweenpublicandprivatepartiesbasedonMethodofMoments(MoM),Aristeidisconstructedamodel

RISK EVALUATION BASED ON GREY FUZZY THEORY 113

to evaluate the financial risk of PPPproject, andmadeaprobabilistic analysisof the riskbasedonsensitivityanalysisandscenarioanalysis(XieandNg, 2013; Carbonara et al. 2014; Pantelias and Zhang 2010).TheaboveresearchesconfirmtheimportanceofPPPprojectriskevaluation(BasakandGajbhiye2018,Yangetal.2018).TheriskresearchofwaterconservancyPPPprojectismainlyofqualitativede-scription.Thereisacertaingapbetweentheexistingevaluationmodel and the actual project operationapplicationatthepresentstage(Shenetal.2017,Xueetal.2016).Thecalculationprocessiscomplicated,andtheevaluationresultisnotclear,whichmakestheriskevaluationofwaterconservancyPPPprojectstillimmature.Therefore,inthispaper,basedongreyfuzzy theory, agrey fuzzycomprehensiveevalua-tionmodelofwaterconservancyPPPprojectwasconstructed, and uncertain grey and fuzzy contents were transformed into values that can be accurately measured,whichprovidedabasisformanagerstomakedecisions(AlbrechtandShaffer2016,Luetal.2017).

CONSTRUCTION OF THE RISK EVALUATION INDEX SYSTEM OF WATER

CONSERVANCY PPP PROJECT

Onthebasisofsummarizingtheexistingrisks,according to the characteristics of water conservancy PPPproject,ariskevaluationindexsystemofwaterconservancyPPPprojectwasdeterminedbyDelphimethod and literature collectionmethod.The riskevaluationindexsystemofwaterconservancyPPPprojectisshowninFig. 1.

DETERMINATION OF THE WEIGHT OF RISK EVALUATION INDEXES OF WATER CONSERVANCY PPP PROJECT BY RANK

CORRELATION ANALYSIS

RankCorrelationAnalysisisasubjectiveweight-ing method combining qualitative and quantitative methods.Indeterminingtheindexweight,AHPneedstoestablishthejudgmentmatrixbyexpertassign-ment, and to meet the consistency requirements, but whenthesampledataarelarge,itisdifficulttomeettheconsistencyrequirements.Therankcorrelationanalysisandconsistencycheckneednottoestablishthejudgmentmatrixandthecalculationisreduced,whichissuitableforthecaseoflargesampledataanddifficulttomakecompletequantitativeanalysis.

Determination of the order relation of risk evalu-ation indexes

Theexpertsrankedtheriskevaluationindexesatthe same level U1, U2, …, Un-1, Un from the most im-portanttotheleast,namely,U1

*> U2*>…> Un-1

*>Un*.

Where Ui*>Uj

*showedthattheriskevaluationindexiwasnot inferior to the riskevaluation index j in importance,thatis,theriskevaluationindexi was superiortoorequaltotheriskevaluationindexj in importance.

Assignment of the degree of importance between risk evaluation indexes

Fortheratioofimportanceribetweenadjacentrisk evaluation indexesU*i-1andU*i at the samelevel, then:

ri = ωi-1/ωi (1)

Whereωi-1andωi were the weights of the i-1th and ithriskevaluationindexes,respectively,ri was usually assigned with 1~2 values. The assignment and evaluation rules for ri are shown in Table I.

Calculation of the weight of risk evaluation in-dexes

According toFormula (1), Formula (2) belowwas obtained:

211

1

2

1

1 ≥== −−

−

−

+

−=∏ kr

n

k

n

n

n

n

k

k

k

kn

ki i ωω

ωω

ωω

ωω

ωω

� (2)

Byfindingthesumofk from 2 to n,Formula(3)below was obtained:

n

knk

n

ki ink r

ωω 1

22 )( −=== ∑=∑ ∏ (3)

Sincethesumoftheweightsofallriskevalua-tionindexeswas1,Formula(4)belowwasobtainedfromFormula(3):

nk

nk

nn

knk

n

n

n

knk

n

ki ink r

ωω

ωωω

ωω

ωω

11

1)(1

11

2

122

=∑=∑+

=∑+=∑+

=−

=

−=== ∏

(4)

ByFormula(4),weknowthattheweightofotherriskevaluationindexescanbededucedbycalculatingtheweightofthelastriskevaluationindexωn. After deformationofFormula(4),Formula(5)belowwasobtained:

B. Wang et al.114

[ ]1-

2 )(1 ∏==∑+=n

ki inkn rω (5)

TheweightofotherriskevaluationindexescanbededucedstepbystepbyFormula(6)below:

ωn-1 = rnωn (6)

Determination of the weight of risk evaluation indexes

TheweightofriskevaluationindexUi* was cal-culatedbyRankCorrelationAnalysis.Accordingtothecorrespondingrelationbetweenriskevaluationindexes andorder relation evaluation indexes, theweightofriskevaluationindexeswasdetermined.

Fig. 1. AriskevaluationindexsystemofwaterconservancyPPPproject

Water conservancy PPP project Technology risk

Organization andappointment

Changes in the distribution of responsibility and power

Communication risk

Duration overrun

Construction safety

Cost overrun

Poor operation quality

Rising maintenance costs

Operating cost overrun

Low operational efficiency

Residual risk

Completion risk

Theats to environmentapublic security

Public opinion risk

Lack of good faith in socialcapital

Political and legal risk

Natural risk

Economic risk

Market risk

Management risk

Relationship risk

Construction risk

Operational risk

Other risk

Legal change

Political stability

Government credit

Government objection

Approval delay

Unfavorable materialconditionForce majeure

Environmental pollution

Inflation

Interest rate risk

Exchange rate risk

Similar project

Market demand change

Design change

Technical applicability

Design quality

Decision risk

Organizational risk

Personnel risk

RISK EVALUATION BASED ON GREY FUZZY THEORY 115

CONSTRUCTION OF THE GREY FUZZY COMPREHENSIVE EVALUATION MODEL OF WATER CONSERVANCY PPP PROJECT

Determination of the risk evaluation index system and its weight

Onthebasisofriskanalysisandriskidentifica-tion,ariskevaluationindexsystemofwaterconser-vancyPPPprojectwasconstructed,andtheweightofriskevaluationindexesofwaterconservancyPPPprojectwascalculatedbyRankCorrelationAnalysis.

Establishment of the fuzzy evaluation set and evaluation sample matrix

Fuzzy evaluation set is a set composedof riskevaluation of risk indexes by experts, which isgenerally expressed asV, that is, V={V1, V2,…, Vh}, where h is thenumberofexperts.IntheriskevaluationofwaterconservancyPPPproject,theriskwasgenerallydividedintofivelevels:smallerrisk,smallrisk,generalrisk,largerisk,largerrisk,andthecorrespondingevaluationgradeVwas:1,3,5,7,9,that is, V=(1,3,5,7,9).Theriskbetweenadjacentlevelswas2,4,6,8.Accordingtotheprobabilityofriskoccurrence inwaterconservancyPPPproject,theexpertsevaluatedtheriskevaluationindexesandestablishedanevaluationsamplematrix.

D =(dij) (7)

Where i=1,2, …,h; j=1,2, … ,m; h was the number ofexperts;m wasthenumberofriskindexes.

Determination of the evaluation grey class and grey evaluation coefficient

IntheriskevaluationofwaterconservancyPPPproject,theriskwasgenerallydividedintofivelevels:smallerrisk,smallrisk,generalrisk,largerisk,largerrisk,andthecorrespondingevaluationgreyclassewas: 1, 2, 3, 4, 5. The whitening weight function is

the degree to which a certain grey number inclines to a certain value within a certain range, and it mainly describesthedegreetowhichanevaluationobjectissubordinatetoacertaingreyclass.Supposeallthewhitening weight functions were linear functions, the greynumbercorrespondingtotherisklevelandthewhitening weight function are shown in Table II.

Todetermine thegreyevaluationcoefficient, itwas necessary to calculate the whitening weight func-tionoftheevaluationvalueintheevaluationsamplematrixaccordingtoTable II.Supposethegreyevalu-ationcoefficientoftheeth evaluation grey class of theriskevaluationindexj by the ithexpertwasxije, thegreyevaluationcoefficientoftheeth evaluation greyclassoftheriskevaluationindexjbytheexpertswas xje,andthegreyevaluationcoefficientoftheriskevaluationindexjbytheexpertswasxj, then:

xije = fe(dij) (8)

TABLE I. THEASSIGNMENTANDEVALUATIONRULESFORrI

ri Evaluation instructions

1.0 U*i-1 isasimportantas U*

i1.2 U*

i-1 and U*iarealittleimportant

1.4 U*i-1 and U*

iarecomparativelyimportant1.6 U*

i-1 and U*iareveryimportant

1.8 U*i-1 and U*

iareparticularlyimportant

Note:1.1,1.3,1.5,1.7and1.9arebetweentwoadjacentscales

TABLE II. THEGREYNUMBERCORRESPONDINGTOTHERISK LEVELANDTHEWHITENINGWEIGHTFUNCTION

Risklevel The grey number

Whiteningweight function

“smallrisk”(e=1) ⊗1 ∈[0,1,4] ( )

[ ][ ]( ]⎪

⎩

⎪⎨

⎧

∈

∈

∉

=

4,11,04,0

/3-3/410

1

ij

ij

ij

ij

ij

ddd

ddf

“smallerrisk”(e=2) ⊗2 ∈[0,3,6] ( )

[ ][ ]( ]⎪

⎩

⎪⎨

⎧

∈

∈

∉

−

=

6,33,06,0

3/23

0

2

ij

ij

ij

ij

ijij

ddd

dddf

“generalrisk”(e=3) ⊗3 ∈[2,5,8] ( )

[ ][ ]( ]⎪

⎩

⎪⎨

⎧

∈

∈

∉

−

−=

8,55,28,2

3/3/83/23/

0

3

ij

ij

ij

ij

ijij

ddd

dddf

“largerrisk”(e=4) ⊗4 ∈[4,7,9] ( )

[ ][ ]( ]⎪

⎩

⎪⎨

⎧

∈

∈

∉

−

−=

9,77,49,4

2/2/93/43

0

4

ij

ij

ij

ij

ijij

ddd

dddf

“greatrisk”(e=5) ⊗5 ∈[5,8,9] ( )

[ ][ ]( ]⎪

⎩

⎪⎨

⎧

∈

∈

∉

−=

9,88,59,5

13/53

0

5

ij

ij

ij

ijij

ddd

ddf

B. Wang et al.116

ijehije xx 1=∑= (9)

ijeehij xx 5

11 == ∑∑= (10)

Where i=1, 2, …,h; j=1, 2, …,m; e=1, 2, 3, 4, 5.

Determination of the membership degree and membership matrix

Themembershipcjeoftheriskevaluationindexjtothegreyscaleewasdetermined,thatis,thegreyevaluationcoefficientoftheriskevaluationindexjwas normalized, then:

ijeehi

ijehi

je xx

c 511

1

==

=

∑∑

∑= (11)

Thefirst-orderfuzzymembershipmatrixCb was:

Tebuebebbjeb b

ccccC ],,,[][ 21 …== (12)

Where b=1, 2, …,s, s was the number of second-levelriskevaluationindexes,andj=1, 2, …, ub, ub was the number of risk evaluation indexes corre-spondingtothesecond-levelriskevaluationindexesinthefirst-levelriskevaluationindexes.

Fuzzy comprehensive evaluationThesecond-levelfuzzycomprehensiveevaluation

was to convert the fuzzy vector Wb on the Ub to the fuzzy vector Bb on the V by fuzzy linear conversion, that is:

Tebuebebbubbbbb bb

cccwwwCWB ],,,][,,,[ 2121 ……== (13)

Thenthejudgmentmatrixwas:

B = [B1, B2, …,Bs] (14)

Similarly, the first-level fuzzy comprehensiveevaluation was to convert the fuzzy vector W on the U to the fuzzy vector R on the V by fuzzy linear conversion, that is:

Tss BBBwwwWBR ],,,][,,,[ 2121 ……== (15)

Analysis of the evaluation resultBymultiplyingthespecificvalueRoffuzzycom-

prehensiveevaluationbythequantitativeevaluationindexvectorV=(1,3,5,7,9), thecomprehensiveevaluation result Q=R·Vofprojectriskwasobtained.Bycomparingtheriskevaluationindexeswiththeresultofcalculation,theriskgradeofwaterconser-vancyPPPprojectwasfinallydetermined.

CASE ANALYSIS

Project overviewFendouReservoirisaproposedwaterconservancy

PPPprojectinHeilongjiangProvinceinrecentyears.The total investment is about 1,426 million yuan, of which, the government contribution is 800 million yuan,andthesocialcapitalis626millionyuan,ac-countingfor43.9%ofthetotalinvestment;thetotalconstructionperiodis36months.FendouReservoir,amajorwaterconservancyprojectwithsocialcapitalparticipating in its construction andoperation,hasgreatlyreducedthenationalfinancialburdenandmadeupforthelackofgovernmentfinancialfunds.Throughinvestmentininfrastructure,thesocialcapitalcanalsoobtain long-term and steady returns.

Risk evaluationEstablishment of the risk evaluation index system

According to the characteristics of Fendou Res-ervoir, a risk evaluation index systemof FendouReservoir PPPprojectwas determined byDelphimethod and literature collectionmethod.The riskevaluation indexsystemofFendouReservoirPPPprojectisshowninTable III.

Determination of the weight of risk evaluation indexes

FiveexpertsinthefieldofwaterconservancyPPPprojectwereinvitedtorankandassignthefirst-levelrisk evaluation indexes of FendouReservoir PPPprojectfromthemostimportanttotheleast.Theorderrelationandratioofimportanceofthefirst-levelriskevaluationindexesareshowninTable III.

Accordingtotheorderrelationofthefirst-levelrisk evaluation indexes, theweight of each indexwascalculatedbytheFormulas(5)and(6).Thecal-culationresultoftheweightofthesecond-levelriskevaluationindexesisshowninTable V.

Similarly, theweight of the second-level riskevaluationindexescanbeobtained.Thecalculationresultoftheweightofthesecond-levelriskevalua-tionindexesisshowninTable III.

Establishment of the evaluation sample matrix and determination of the evaluation grey class

To evaluate the risk ofFendouReservoirPPPproject,fiveexpertsinthefieldofwaterconservancyPPPprojectwereinvitedtoranktheriskevaluationindexesonascaleof1to9.Accordingtotheformulaofwhiteningweightfunctionandtheresultofexpertscoring, thegreyevaluationcoefficientof the riskevaluation indexeswas calculated.The scoringof

RISK EVALUATION BASED ON GREY FUZZY THEORY 117

TABLE III. THERISKEVALUATIONINDEXSYSTEMOFFENDOURESERVOIRPPPPROJECT

Target layer Criterion layer Weight Indexlayer Weight

Riskevaluation indexesof Fendou ReservoirPPPproject

Political and legalriskU1

0.208

Legal change U11 0.201 Political stability U12 0.135 Government credit U13 0.283 GovernmentobjectionU14 0.194ApprovaldelayU15 0.187

Naturalrisk U2 0.092Unfavorable material condition U21 0.306 ForcemajeureU22 0.358 EnvironmentalpollutionU23 0.336

Economicrisk U3 0.173

InflationU31 0.263 InterestrateriskU32 0.190ExchangerateriskU33 0.195FinancingriskU34 0.244 TaxriskU35 0.109

MarketriskU4 0.062 SimilarprojectcompetitionU41 0.437MarketdemandchangeU42 0.529

Technologyrisk U5 0.031DesignchangeU51 0.380 TechnicalapplicabilityU52 0.345 DesignqualityU53 0.276

ManagementriskU6 0.109DecisionriskU61 0.360 OrganizationalriskU62 0.338 PersonnelriskU63 0.302

RelationshipriskU7 0.07ChangesinthedistributionofresponsibilityandpowerU71 0.370OrganizationandappointmentU72 0.314 CommunicationriskU73 0.317

ConstructionriskU8 0.039Construction safety U81 0.298DurationoverrunU82 0.308 Cost overrun U83 0.394

OperationalriskU9 0.117

OperatingcostoverrunU91 0.299Rising maintenance costs U92 0.169PooroperationqualityU93 0.148 LowoperationalefficiencyU94 0.175ResidualriskU95 0.209

OtherriskU10 0.098

CompletionriskU101 0.185 ThreatstoenvironmentalpublicsecurityU102 0.222 PublicopinionriskU103 0.297LackofgoodfaithinsocialcapitalU104 0.295

TABLE IV. THEORDERRELATIONANDRATIOOFIMPORTANCEOFTHEFIRST-LEVELRISKEVALUATIONINDEXES

No. Theorderrelationofindexes r2 r3 r4 r5 r6 r7 r8 r9 r10

1 U1 >U3 >U9>U4 >U7>U2 =U10 >U6 >U8 >U5 1.5 1.3 1.2 1.3 1.2 1 1.3 1.2 1.32 U3 >U6 >U2 >U7>U10 >U4 >U8 >U9>U1 >U5 1.1 1.5 1.7 1.3 1.2 1.5 1.3 1.6 1.23 U4 >U3 >U1 >U9>U7>U6 >U2 >U10 >U8 >U5 1.6 1.2 1.6 1.6 1.8 1.2 1.4 1.2 1.44 U1 =U5 = U9>U8 >U10 >U4 >U7>U6 =U3 >U2 1 1 1.7 1.5 1.2 1.5 1.2 1 1.75 U1 >U9>U2 >U4 >U10 >U3 >U7>U8 >U6 >U5 1.5 1.7 1.2 1.5 1.5 1.3 1.2 1.3 1.3

B. Wang et al.118

theriskevaluationindexesandthecalculationresultare shown in Table VI.

Fuzzy comprehensive evaluation(1) Second-level fuzzy comprehensive evaluation

ByFormula(13),thecomprehensiveriskevalua-tionundertheriskindexUi was calculated:

Similarly,byFormula(11),thefuzzyvariableonthesecond-levelriskevaluationindexwascalculated:

] 0.068 0.145 0.238 0.292 257.0[240.0360.0320.0080.0000.0000.0083.0417.0417.0083.0000.0000.0042.0417.0542.0000.0000.0000.0350.0650.0115.0308.0423.0154.0000.0

187.0194.0283.0135.0201.0

111

=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=×=

T

CWB(16)

Similarly, the fuzzy variable Bon the second-level riskevaluationindexeswascalculatedbyFormulas(11):

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

045.0133.0270.0318.0233.0000.0012.0172.0482.0333.0000.0040.0272.0492.0197.0031.0046.0235.0476.0215.0000.0000.0156.0500.0344.0000.0000.0146.0462.0393.0035.0128.0371.0341.0092.0026.0087.0147.0360.0379.0027.0106.0327.0359.0181.0068.0145.0238.0292.0257.0

10

9

8

7

6

5

4

3

2

1

BBBBBBBBBB

B (17)

(2) First-level fuzzy comprehensive evaluationByFormula (15), the calculation result of the

first-level fuzzy comprehensive evaluationwasR=W•B=[0.2760.3860.2230.0820.030],thegradevector of the evaluation grey class was V=(1,3,5,7,9)T,andthecomprehensiveevaluationresultwasQ=R•V=3.398.

Analysis of the evaluation resultThecomprehensiveevaluationvalueofFendou

ReservoirPPPprojectwas3.398,whichbelongedto small risk, thus itwas feasible.Themain risksof the PPP projectwere political and legal risksand economic risks,whichwill directly affect thesmoothprogressof thewholePPPproject.There-fore,great importanceshouldbeattached to themandcorrespondingriskcountermeasuresshouldbeworkedout..

CONCLUSIONS

In this paper, a quantifiablemethod for riskevaluationofwater conservancyPPPprojectwaspresented.Firstly, according to the characteristicsofwaterconservancyPPPproject,ariskevaluationindexsystemofwaterconservancyPPPprojectwasdeterminedbyDelphimethodandliteraturecollec-tionmethod;secondly,theweightofriskevaluationindexesofwaterconservancyPPPprojectwasdeter-minedbyRankCorrelationAnalysis;thirdly,basedongreyfuzzytheory,agreyfuzzycomprehensiveevaluationmodelofwaterconservancyPPPprojectwas constructed. Finally, the grey fuzzy compre-hensive evaluationmodelwas applied to FendouReservoir,awaterconservancyPPPproject,anditprovedtobereasonableandscientificbecausetheevaluationresultsweremoreobjective,impartialandscientificforitcaneffectivelyreducetheinfluenceofhumanfactorsintheevaluation,thusmakingthedecision-makingmorescientific.

ACKNOWLEDGMENTS

TheauthorsaregratefultothesupportofNationalNaturalScienceFoundationofChina(No.51709116,No.51579101), theKeyScientificResearchProj-ects of Henan Province Universities and Colleges

TABLE V. THECALCULATIONRESULTOFTHEWEIGHTOFTHESECOND-LEVELRISKEVALUATIONIN-DEXES

number w1 w2 w3 w4 w5 w6 w7 w8 w9 w10

1 0.25 0.128 0.044 0.107 0.068 0.166 0.034 0.068 0.053 0.0822 0.16 0.06 0.241 0.04 0.016 0.094 0.031 0.019 0.265 0.0733 0.107 0.171 0.328 0.018 0.031 0.037 0.205 0.013 0.022 0.0674 0.2 0.079 0.036 0.036 0.021 0.118 0.044 0.065 0.2 0.25 0.325 0.023 0.216 0.106 0.018 0.127 0.036 0.03 0.047 0.071

weight 0.208 0.092 0.173 0.062 0.031 0.109 0.07 0.039 0.117 0.098

RISK EVALUATION BASED ON GREY FUZZY THEORY 119

(No.17B570003),DistinguishedYoungScholar ofScienceandTechnologyInnovation(184100510014)andFoundationforDrinNorthChinaUniversityofWaterResources andElectricPower (No.10030).Specialthanksforthereviewersandtheirconstruc-tive comments and suggestions in improving thequalityofthismanuscript.

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