数学建模灰色关联度分析英文版

1、4.1 GreyRelationalAnalysisFirst,selectareferencesequenceasshownbelow:X0='：Xok|k=1,2,n)=x。1,x02,x。nAndtheothergroupofsequenceis,Xi-'.Xik|k=1,2,n；H：x1,X2,xn,i=1,2,mThenthecorrelationdegreeofxitox0is,riInwhich,msinmtinxot-xst?maxmtaxxot-x$tx。t-xst?maxmaxxot-xstThen,weuseritodescribethecorrelati

2、ondegreebetweenxiandx。,namelytodescribetheinfluenceonx。causedbythechangeofxi.Ingeneral,Practicalproblemsoftenhavedifferentnumbersofdifferentdimension,butwhenwecalculatethecorrelationdegree,itrequiresthesamenumbersofsamedimension.Sowewanttocarryoutavarietyofdataprocessingdimensionless.inaddition,Forc

3、omparisoneasily,allthesequsecesarerequiredtohaveacommonpoint.Inordertosolvethesetwoproblems,wetransformthegivensequences.Thegivensequencex=x1,x2,xnii,wenameasinitializationsequenceofOriginalsequencex=x1,x2,xn)1x3,x1,x1x(n4.2 WaterresourcescarryingcapacityevaluationindexesandclassificationindexesThee

4、stablishmentofevaluationindexsystemofwaterresourcescarryingcapacityisakeyissueinthestudyofwaterresourcescarryingcapacity.Regionalwaterresourcescarryingcapacityisinfluencedbymanyfactors,Shouldbeselectedaccordingtotherequirementsofthespecificregionalsocialdevelopmentbacklogofsocial-economicindexsystem

5、response-naturalcompoundecosystemdevelopmentscaleandquality,referenceexistingliteratureresults,throughthegreycorrelationanalysis,thebearingcapacityofwaterresourcesevaluationindexareshownintable1.ApproachA:WeightedAverageEvaluationBasedModelFig.1.Theindexsystemofwaterresourcescarryingcapacity>Comp

6、rehensiveanalysisofwaterresourcescarryingcapacityofmaininfluencingfactorsandperformancesystem,withreferencetotheevaluationindexsystemofwaterresourcescarryingcapacityathomeandabroadtoselectthefollowing6mainfactorsasevaluationfactors,Themeaningofthefactorsasfollows:Waterresourceutilizationratio(u1):wa

7、terandtheratioofthetotalpopulation(m/人)；waterutilizationrate(u2):Theratiooftheavailablewaterquantityandwaterresources(%);utilizationrateofarableland(u3):Irrigationareaandmoreontheratioofthearea(%);43,2Themodulusofwatersupply(4):waterandtheratioofthelandarea(10m/km);modulusofwaterrequirement(5):Theto

8、talwaterdemandandtheratioofthelandarea(104m3/km2);Lifewateruseratio(u6):Domesticwateramountandtheratioofthetotalwaterdemand(%)AccordingtotheabovesixevaluationfactorsontheinfluencedegreeoftheregionalwaterresourcescarryingcapacityWilltheinfluenceofthesefactorsaredividedintothreelevels,Eachfactor,thenu

9、mberofeachlevelindicatorsareshownintable2.Thesaidconditionisbad,waterresourcescarryingcapacityisclosetosaturationvalue,furtherdevelopmentandutilizationofpotentialissmaller,developwatershortageswilloccur;Membershipconditionisgood,saidtherearestilllargecarryingcapacityofwaterresourcesinthisarea,waterr

10、esourceutilizationdegreeofdevelopmentinthisareaaresmall,watersupplysituationmoreoptimistic;Levelisbetweentheabovetwolevels,whichindicatesthatthisareahasascaledevelopmentforthesupplyofwaterresourcesdevelopment,butstillhasacertainabilityofdevelopmentandutilizationoflocaleconomicdevelopmentandpeoplehav

11、ecertainguaranteesurvival.TheevaluationfactorsViV2V3m3人-1>22502250-1000<1000Percapitawatersupply/1/Waterresourcesutilization%<3030-60>60Themodulusofwatersupply/<8080-100>100432、10m(km)Farmlandirrigationrate/%<2020-50>50Waterdemandmodulus/<6060-100>100432、10m(km)Domestic

12、waterrate/%>44-2<20.950.50.05,a；ScoresjTable2:classificationindexcomprehensiveevaluationfactors4.3ThefuzzycomprehensiveevaluationmodelBecauseofthebearingwithuncertaintyandfuzziness,thefuzzyevaluationmodelcanbewellcarriedoutonthewaterresourcescarryingcapacitymulti-factorandmulti-levelcomprehens

13、iveevaluation,comprehensivetoreflectthestatusoftheregionalwaterresourcescarryingcapacity.FuzzyevaluationforB=AR_(Ui%V=(Ki也.r,"一finitefield-,-,WithUonbehalfofthecomprehensiveevaluationfactorsofcollection,Vonbehalfoftheevaluationofcollection.TypeAisUinthefuzzysubsetCEWA,£1,Q；A=-,0-一forUforAm

14、embership.Itmarkedthesinglefactorevaluationfactorsintheroleofsize,Toacertainextent,alsoonbehalfoftheratings;TheevaluationresultB如bj.b.n与乐二1isthefuzzysubsetofV.B=,0,forthelevelofcomprehensiveevaluationthemembershipdegreeoffuzzysubsetB,theysaytheresultofcomprehensiveevaluation.Evaluationmatrixrltr12er

15、>_21?整,工T2n*nrin2斤UtlTfltlTthtjAmongrjforUievaluationofgradeR=(ri1ri2.rin)membershipdegree,Matrixoftheithlineisthesinglefactorevaluationresultsoftheithafactor.EvaluationcomputermatrixArepresentativeofthevariousfactorsonthecomprehensiveevaluationoftheimportanceofweightcoefficient,thussatisfy,fuzzy

16、transformARalsocanbedegradedforcommonmatrixiscalculated.4.3.1ThecalculationofmatrixRCorrespondstotheevaluationsetsofevaluationfactors,andcanbethroughtheevaluationfactorsintheevaluationmatrixRtheactualnumericalcontrolclassificationindexesofvariousfactorstoanalysisandcalculation.Inordertomakethemember

17、shipfunctioncansmoothtransitionbetweenatalllevels,theblurprocessing.OfV2pointofmembershipdegreeis0.5,themidpointtoaccordingtolinearregressiveprocessing.ForV1andV3onbothsidesoftheinterval,thenmakethefartherawayfromthecriticalvalueofrangeoneithersideofthemembershipdegree,thegreaterthebelongtobothsides

18、onthecriticallevelofmembershipyou0.5accordingtothegradesoftheaboveideastoconstructaevaluationthecalculationformulaofsubordinatefunction.V1andV2levelthresholdforK1,V2andV3thresholdforK3,V2mid-rangelevelintervalforK2.K2.Forevaluatingfactorsu3u4u5u6andcommentsandcalculatingformulaforrelativemembershipd

19、egreefunction:0.5(1+u")ui<k1k2-uiUvi=0.5(1-u-必)k1<ui:二k2(1)k2-k100.5(1-k)ui<k1k2-uiQ)0.5(1+-)k1Muj<k2k2-k1uv2=5k0.5(1+3)k1<ui<k3k3一女20.5(1uJ_)ui之k3.k3-uj0.5(1+u)Ui>kak2UiUv3=0.5(1一曳马k2<Ui:二k3(3)k2-ka0Ui<k2CalculatetherelativemembershipdegreeofevalUationfactorsaccordin

20、gtothetype,'-K，-1：ForevalUationfactorsL-'intheevalUationandthecalcUlationoftherelativemembershipdegreefUnctionsimplytype(1)(3)therightendoftypeUIintervalgood"-"insteadof"-"And"<"insteadof">"afterthecalcUlationformUlaofthesame4.3.2FUzzycomprehensiveevalUationAccordingtotheevalUationfactorsinflUencethesizeo