数学建模灰色关联度分析英文版.docx

数学建模灰色关联度分析英文版.docx

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4.1GreyRelationalAnalysis

First,selectareferencesequenceasshownbelow:

Andtheothergroupofsequenceis,

Thenthecorrelationdegreeoftois,

Inwhich,

Then,

weusetodescribethecorrelationdegreebetweenand,namelytodescribetheinfluenceoncausedbythechangeof.

Ingeneral,Practicalproblemsoftenhavedifferentnumbersofdifferentdimension,butwhenwecalculatethecorrelationdegree,itrequiresthesamenumbersofsamedimension.Sowewanttocarryoutavarietyofdataprocessingdimensionless.inaddition,Forcomparisoneasily,allthesequsecesarerequiredtohaveacommonpoint.Inordertosolvethesetwoproblems,wetransformthegivensequences.Thegivensequencewename

asinitializationsequenceofOriginalsequence

4.2Waterresourcescarryingcapacityevaluationindexesandclassificationindexes

Theestablishmentofevaluationindexsystemofwaterresourcescarryingcapacityisakeyissueinthestudyofwaterresourcescarryingcapacity.Regionalwaterresourcescarryingcapacityisinfluencedbymanyfactors,Shouldbeselectedaccordingtotherequirementsofthespecificregionalsocialdevelopmentbacklogofsocial-economicindexsystemresponse-naturalcompoundecosystemdevelopmentscaleandquality,referenceexistingliteratureresults,throughthegreycorrelationanalysis,thebearingcapacityofwaterresourcesevaluationindexareshownintable1.ApproachA:

WeightedAverageEvaluationBasedModel

Fig.1.Theindexsystemofwaterresourcescarryingcapacity

Agricultureinvestment

Socialeconomicindicator

indicators

Industryinvestment

PerGDP

Theindexsystemofwaterresourcescarryingcapacity

Waterenvironmentindicator

Waterresourcesindicators

Industrialsewagetreatment

Irrigationdisplacement

Percapitalemission

Lifewaterlever

Waterresourcequantity

Comprehensiveanalysisofwaterresourcescarryingcapacityofmaininfluencingfactorsandperformancesystem,withreferencetotheevaluationindexsystemofwaterresourcescarryingcapacityathomeandabroadtoselectthefollowing6mainfactorsasevaluationfactors,Themeaningofthefactorsasfollows:

Waterresourceutilizationratio（）:

waterandtheratioofthetotalpopulation（）;

waterutilizationrate（）:

Theratiooftheavailablewaterquantityandwaterresources（%）;

utilizationrateofarableland（）:

Irrigationareaandmoreontheratioofthearea（%）;

Themodulusofwatersupply（）:

waterandtheratioofthelandarea（）;

modulusofwaterrequirement（）:

Thetotalwaterdemandandtheratioofthelandarea

（）;

Lifewateruseratio（）:

Domesticwateramountandtheratioofthetotalwaterdemand（%）

AccordingtotheabovesixevaluationfactorsontheinfluencedegreeoftheregionalwaterresourcescarryingcapacityWilltheinfluenceofthesefactorsaredividedintothreelevels,Eachfactor,thenumberofeachlevelindicatorsareshownintable2.Thesaidconditionisbad,waterresourcescarryingcapacityisclosetosaturationvalue,furtherdevelopmentandutilizationofpotentialissmaller,developwatershortageswilloccur;Membershipconditionisgood,saidtherearestilllargecarryingcapacityofwaterresourcesinthisarea,waterresourceutilizationdegreeofdevelopmentinthisareaaresmall,watersupplysituationmoreoptimistic;Levelisbetweentheabovetwolevels,whichindicatesthatthisareahasascaledevelopmentforthesupplyofwaterresourcesdevelopment,butstillhasacertainabilityofdevelopmentandutilizationoflocaleconomicdevelopmentandpeoplehavecertainguaranteesurvival.

Theevaluationfactors

Percapitawatersupply/

>2250

2250--1000

<1000

Waterresourcesutilization%

<30

30--60

>60

Themodulusofwatersupply/

<80

80--100

>100

Farmlandirrigationrate/%

<20

20--50

>50

Waterdemandmodulus/

<60

60--100

>100

Domesticwaterrate/%

>4

4--2

<2

Scores

0.95

0.5

0.05

Table2:

classificationindexcomprehensiveevaluationfactors

4.3Thefuzzycomprehensiveevaluationmodel

Becauseofthebearingwithuncertaintyandfuzziness,thefuzzyevaluationmodelcanbewellcarriedoutonthewaterresourcescarryingcapacitymulti-factorandmulti-levelcomprehensiveevaluation,comprehensivetoreflectthestatusoftheregionalwaterresourcescarryingcapacity.

Fuzzyevaluationfor

B=AR

finitefield,,WithUonbehalfofthecomprehensiveevaluationfactorsofcollection,Vonbehalfoftheevaluationofcollection.TypeAisUinthefuzzysubset

A={},0forUforAmembership.Itmarkedthesinglefactorevaluationfactorsintheroleofsize,Toacertainextent,alsoonbehalfoftheratings;TheevaluationresultBisthefuzzysubsetofV.B={},0,forthelevelofcomprehensiveevaluationthemembershipdegreeoffuzzysubsetB,theysaytheresultofcomprehensiveevaluation.

Evaluationmatrix

Amongforevaluationofgrademembershipdegree,Matrixoftheithlineisthesinglefactorevaluationresultsoftheithafactor.

EvaluationcomputermatrixArepresentativeofthevariousfactorsonthecomprehensiveevaluationoftheimportanceofweightcoefficient,thussatisfy,fuzzytransformARalsocanbedegradedforcommonmatrixiscalculated.

4.3.1ThecalculationofmatrixR

Correspondstotheevaluationsetsofevaluationfactors,andcanbethroughtheevaluationfactorsintheevaluationmatrixRtheactualnumericalcontrolclassificationindexesofvariousfactorstoanalysisandcalculation.Inordertomakethemembershipfunctioncansmoothtransitionbetweenatalllevels,theblurprocessing.OfV2pointofmembershipdegreeis0.5,themidpointtoaccordingtolinearregressiveprocessing.ForV1andV3onbothsidesoftheinterval,thenmakethefartherawayfromthecriticalvalueofrangeoneithersideofthemembershipdegree,thegreaterthebelongtobothsidesonthecriticallevelofmembershipyou0.5accordingtothegradesoftheaboveideastoconstructaevaluationthecalculationformulaofsubordinatefunction.V1andV2levelthresholdforK1,V2andV3thresholdforK3,V2mid-rangelevelintervalforK2.K2.

Forevaluatingfactorsu3u4u5u6andcommentsandcalculatingformulaforrelativemembershipdegreefunction:

Calculatetherelativemembershipdegreeofevaluationfactorsaccordingtothetype,Forevaluationfactorsintheevaluationandthecalculationoftherelativemembershipdegreefunctionsimplytype

（1）~（3）therightendoftypeUIintervalgood""insteadof"";And"<"insteadof">"afterthecalculationformulaofthesame

4.3.2Fuzzycomprehensiveevaluation

AccordingtotheevaluationfactorsinfluencethesizeofthecarryingcapacityofwaterresourcesWilljudgefactorsinfluenceonwaterresourcescarryingcapacityendowedwithdifferentweightsAccordingtothematrixAandR,B=ARaccordingtocommonmatrixcalculationrulescanbeobtainedbymatrixofultimatebearingcapacityofwaterresourcesevaluationresults,accordingtothecorrespondingclassificationindexscorevaluesregionalwaterresourcescarryingcapacitycomprehensiveevaluationvaluecanbeobtained,RegionalwaterresourcescarryingcapacitycomprehensiveevaluationvaluecanbeobtainedTheregionalwaterresourcescarryingcapacity.

Thecomprehensiveevaluationandanalysis.Kvalueistohighlighttheroleofthedominantlevel,usuallytake1inaridareas.