一种基于改进灰关联度的变权系数组合预测模型徐凤

2014835JournalofBengbuCollegeOct.2014Vol.3No.52014－05－26*KJ2013B00613CTJ006ACJYYB2013066。1980－。*233030通过引入诱导有序加权调和平均(IOWHA)算子，提出基于改进灰关联度的IOWHA算子组合预测模型，并给出了优性组合预测模型的概念。此组合预测模型是一种变权系数组合预测模型，可以克服传统组合预测方法赋予不变的加权平均系数和以单一误差衡量预测精度的缺陷。最后给出实例说明新方法能有效提高组合预测精度。组合预测;改进灰关联度;IOWHA算子;变权系数F224．3A201405－0028－05ChangingWeightCombinationForecastingModelBasedonImprovedGreyIncidenceXUFeng*CAIXiao-weiYUANHong-junSchoolofStatisticsandAppliedMathematicsAnhuiUnivercityofFinanceandEconomicsBengbu233030AnhuiAbstractBasedoninducedorderedweightedharmonicaveragingIOWHAoperatoraweight-changedcombinationforecastingmodelwasproposedandtheconceptionofsuperiorcombinationforecastingmodelwasgiven．Themodelisachangedweightfactorsmodelwhichcanovercomesomedeficienciesinweigh-tingandusingsingleerrorindexasforecastingprecisionmeasureoftraditionalcombinationforecastingmodel．Finallyanexamplewasillustratedtoshowthatthenewmodelcanimproveforecastingprecisioneffectively．KeywordscombinationforecastingimprovedgreyincidenceIOWHAoperatorchangingweightBates．J．M．Granger．C．W．J．19691。1988YagerOWA2。。2004OWHAIOWHAIO-WHA3。。、。。3。5IOWHAIOWHA。。DOI:10.13900/j.cnki.jbc.2014.05.00811∶13HW∶Ｒm→ＲmW=w1w2…wmTHW∑mi=1wi=1wi≥0i=12…mHWa1a2…an=1∑mi=1wibi1bia1a2…amiHWOWHA。1OWHAa1a2…ammwiaia1a2…amibi。OWHA、、、W=1m1m…1mTOWHA。23m〈u1a1〉〈u2a2〉…〈umam〉ai＞0i=12…mW=w1w2…wmTOWHA∑mi=1wi=1wi≥0i=12…mHW〈u1a1〉〈u2a2〉…〈umam〉=1∑wiau－indexi2WHWHWu1u2…ummIOWHA。u－indexiu1u2…umiuiai。2IOWHAwiaiu1u2…una1a2…an。xtt=12…Nmxititi=12…m．mL=l1l2…lmT∑ni=1li=1li≥0i=12…m．3ait=1－|xt－xitxt||xt－xitxt|＜10|xt－xitxt|≥1i=12…mt=12…N．3aitit。ait∈01．xitait〈a1tx1t〉〈a2tx2t〉…〈amtxmt〉mt。ma1ta2t…amta－indexiti。IO-WHA4。4x^t=IOWHA〈a1tx1t〉〈a2tx2t〉…〈amtxmt〉=1mi=1lixa－indexit4x^tta1ta2tamtIOWHA。4。。5et=1xt－1xteit=1xit－1xiitêt=1x^t－1x^IOWHAti=12…mt=12…N．x－i=11NNi=11xitx=11NNi=11xtx=11NNi=11xtxa－indexit=11NNi=11xa－indexitea－indexit=1xa－indexit－1xa－indexit．tIOWHAêt=1xi－1xi=mi=1li1xa－indexit－1NNt=11xi92=mi=1li1xa－indexit－1NNt=1mi=1li1xa－indexit=mi=1li1xa－indexit－mi=1li1NNt=11xa－indexit=mi=1li1xa－indexit－1xa－indexit=mi=1liea－indexit56γi=1N－1N－1t=111+|a1xt－a1xit|/σxtσxitγ=1N－1N－1t=111+|a1xt－a1xt|/σxtσxt6γiiγIOWHA。a1xta1xita1xt1xt1xit1xt1xt1xit1xtσxtσxitσxt。65a1xt=1xt+1－1xt=1xt+1－1x－1xt－1x=et+1－et7a1xit=1xit+1－1xit=1xit+1－1xi－1xit－1xi=eit+1－eit8a1x^t=1x^t+1－1x^t=1x^t+1－1x^－1x^t－1x^=êt+1－êt9=mi=1liea－indexit+1－ea－indexitσxt=1NNt=1e2槡tσxit=1NNt=1e2槡itσx^t=1NNt=1ê2槡t=1NNt=1Mi=1liea－indexit槡2102IOWHAE=Eijm×mmIOWHAEij=Nt=1eindexitea－indexjtij=12…mL=l1l2…lmTNt=1mi=1liea－indexit2=Nt=1mi=1mj=1liljea－indexitea－indexjt=mi=1mj=1liljNt=1ea－indexitea－indexjt=mi=1mj=1liljEij=LTEL117－116γ=1N－1N－1t=111+N|et+1－et－mi=1liea－indexit+1－ea－indexit|Nt=1e2槡tLT槡EL1212IOWHAγl1l2…lmTγl1l2…lm。。1。IOWHAmaxγl1l2…lt=1N－1N－1t=111+N︳et+1－et－mi=1liea－indexit+1－ea－indexit|Nt=1e2槡tLT槡EL130320141035177γl1l2…lm＜γminl1l2…lmγmin≤γl1l2…lm≤γmaxγl1l2…lm＞γmax。γmin=minγii=12…mγ=maxγii=12…mγl1l2…lmIO-WHA0≤γl1l2…lm≤1。IOWHA。3421980－19871。112345678xt156．40140．40115．9066．6645．9017．9013．4029．20x1t158．63137．2498．2161．3132．6417．4216．4026．47x2t163．5139．5100．465．3835．0215．207．8121．75x3t158．97128．9984．7448．6421．669．3810．7032．23a1t0．97390．97750．84740．91970．71110．97320．77610．9065a2t0．94240．99360．86630．98080．76290．84920．58290．7449a3t0．97170．91870．73110．72970．47190．52400．79850．89625IOWHAx1=1/l1/158．63+l2/158．97+l3/163．5x2=1/l1/139．5+l2/137．24+l3/128．99x3=1/l1/100．4+l2/98．21+l3/84．74x4=1/l1/65．38+l2/61．31+l3/48．64x5=1/l1/35．02+l2/32．64+l3/21．66x6=1/l1/17．42+l2/15．2+l3/9．38x7=1/l1/10．7+l2/16．4+l3/7．812x8=1/l1/26．47+l2/32．23+l3/21．75l1l2l3IOWHAIOWHA13LINGOl1=0．8289l2=0．1611l3=0．01．tIOWHA2。2IOWHA12345678xt156．40140．40115．9066．6645．9017．9013．4029．20xt158．70139．0199．8664．4634．4016．8811．2927．19γ1=0．9736γ2=0．7951IOWHAγ=0．8972γ＞maxγ1γ27IOWHA。4、IOWHA、43。133SSEMAEMAPE1559．65766．20500．11422534．15106．64230．159532119．400012．92380．24414507．70946．04830．1088227．85591．04780．027934。1BatesJMGrangerCWJ．CombinationofforecastsJ．OperationsＲesearchQuarterly1969204451－468．2YagerＲＲ．Onorderedweightedaveragingaggregationop-eratorsinmulticriteriadecisionmakingJ．IEEETransac-tionsonSystemsManandCybernetics1988181183－190．3．IOWHAJ．200412535－40．4．J．2006921－8．5．J．200221258－62．6．M．2008．7．J．19992341－4．8．J．2004341130－134．9．IOWAJ．200322661－65．10．IOWGAJ．201019633－櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐櫐38．1910510ku104104～105100ku10ku。210ku0.22%10ku。2/%12．09100ku1．86100ku10．0210ku9．4510ku0．223、。100ku0.4Mpa、40min10ku0.3Mpa、30min。10ku9.45%。1．M．1978214．2．J．20072528l－84．3．J．200332368－72．4ChatchaiThetsrimuangSaranyuKhammuangKhajeelakChiablaemetal．AntioxidantpropertiesandcytotoxicityofcrudepolysaccharidesfromLentinuspolychrousLévJ．FoodChemistry20111283634－639．5．、D．2008．6．D．2011．7KuiZhongQiangWangYinHeetal．Evaluationofradi-calsscavengingimmunity－modulatorandantitumoractivi-tiesoflonganpolysaccharideswithultrasoniconinS180tumormicemodelsJ．InternationalJournalofBiologicalMacromolecules201047356－60．8．J．2003148495－496．232014103517