計測自動制御学会東北支部第1郎回研究集会（19弧12．13）
資料番号165一丁LCAの総合評価：
定性的及び定量的な基準に対する拡張AHP法
ComprehensiveevaluationofLCA：AnextendedAHPmethod

Wi七hqualitativeandquantitativecriteria○劉震，猪岡光OzhenLiu，HikaruInooka
東北大学大学院情報科学研究科

Gra・duateSclm0lofInformationSciences，Tohok11University
キーワード：階層化意思決定法〔AnalyticlIierar血yProcess），ライフサイクルアセスメント（LifeCycleAssessment），定性的な基準（qllalitativecrterion），定量的な基準（quantitativecriteriozl），評価（evaluation）
連絡先：〒980・77 仙台市青葉区荒巻字青葉東北大学情報科学研究科システム情報科学専攻
副菜，Tel・：（022）217−7021，FaxL＝（022）217r7019，E−nai1：1itlZlhez14contr01．i5．七ohc．ktL．＆C．jp

1．Introduction
EnvironmentprotectionhaBbeenbecomlngan
importantissueformodernind11Stry．LCAisone
OfthemostaL：tivelycon自ideredtcclmiquesforthe
studyandasses台mentOfstrategiestomeetenviron−Fig. 1 Traditional LCA method

mentalchal1enges．LCApresent＄amultir乱ttribllte

decisiDn prOblemwith the goalof amvlng at a

Forq11antitativefactorsMMisanidealmethod．

Slngle meaBure Ofperformance．TraditionalLCA

Bec乱uSe Of the（：0＄tS Of factors can be foundin

metllOdscanbecate即ri2＝ediIltOtWOtyPeSOfcon−
makets，theresultofeva］uationwillbeex乱Ct．But
Ver苫ion：（1沖馴好打m瓜如冊，和Clla占〟即1ef血如几

forqualitativehctorswiththemethodofMM，the膿血叫MM）；（2）用Juemeα紬γeme叫SuCha占肌情−

accllraCyandreliabilitywi11bea鮎cted．Infact，

AltributeUtiLityJ4naly8i＆（MAUA）and＾nalylicHi，erarchyProces8（AHP）1）．htr乱ditionalLCAm。th−

many environmentalgoals generally do nothaveWe）1de触edor agreed upon costs．Although

Ods，allfa，CtOrSareeithertransfbrmedintomoney

examlnlng the socialcost＄，related health costs，（e・g・MM），Ormea飢redinto畠OmeVdue（e■g・AHP

anddirectmarketcostsincurredbyvariousactivi−andMAUA）uni払rmly（畠eeFigurel）・

ties，aVa］uewhichismeaningfu1insome畠it11ations−1−

canbeex七racted，b11tteChniq11eSfordetermingdol− tion（1）〕issetllPtOCarTyOutpairwisecomparisons
larequivalentsofenvironmentalfactorshavenot

ofthe rel且tiveimportanceofthefactor＄With re−yetre乱Chedamaturestateofdevelopmentl−2）・

specttoobjectivesofthehigherlevel・ウー勒恥l／ノ．︸−

明叫

■1′／／

ひ旭Ⅷ帆

¶n叫・・・・・・／

旭・■・・・・′′

tivejudgments，l几

intovaluesuniformlyaL：COrdingtolluma．n ssubjec−

U2

tor＄（includingquantitativefactors〕axemeasured

W1

MAUA，prOblem畠eXistinaccuracythatal1thefac．

′ノ／・・・・・・′′

At tlle Same time，forthe methods ofAIIP andItisinterpreteda占follo耶＝eVeryelement，aij，

Inth主spaperlthecomprehen8iveevaluationwith
quantitativeand qualitativef乱亡tOrSis con＄idcredヽofthematrix A sl10WSthe relativecontribution−
tothesubjectofcomparison¶Ofttleithactivity

and an extended AHP methad with respect to it

乱S亡Omparedtothejtha・Ctivity，i・e

isproposed・AnexampleofLCAwi11beusedto

叫＝叫／叫 1≦i≦陀，1≦j≦n・illustratetheextendedAHP method．

（2）

Wherewi，i＝1，2，・・・，nPreSent畠theweightof

2．The Axioms ofThe AHP

factori．ThescalehrenteringjudgmentsisglVenTheaxi。mS。fAHP6）callberepresenteda5

もySaaty6〕sb珊na眉Tablel・threepart＄：（1）deeomposing，（2）comparativejudg−
ing，amd持）ー弧bng・

InageneraldecisionmakingenvironmentIitis
di侃culttogettheprecisevaluesofthe叫／wjbut

In part〔11，decision problemis decompoBed

into a geries ofsmal1er problem＄．The goalde一

onlyestimatesofthem・Letusconsiderestimatesof

thesevaluesgivenbyandeci＄ionmal（er（oragroup

嵐11edatthehighestleveli＄brokendownintonlea−ofdecisionmakers）whomaymal（e8mallerrorsinsures（attributes）whicha鮎ctit・Eachofthesejudgment．Ac亡Ordingtotheeigenvaluetheory6），

attribute良Caninttlrnbefurtherdecomposedinto

asmal1perturbation aroundasimple el酢nValue，subLat，tributes．At thelowe呂tlevelof these at，aswehaveinnwheIIAisconsistent，lead畠trOan

trilmtes，knownaBalternatives，aretheproposed

elgenValueproblem oftheformofj4w＝入ma＆products or strategiesin question whicharethe

where入ma苫i与theprlnCipaleigenvalueofAwIlere

subjectofthe胃t11dyinthattheyarethepossibleAmaynolongerbeconsi＄tentb11tisstillreclprD−approaehestoachievingthegoal・

cal．Forthe亡OnSistencyindex（CI），WeadopttheInpart（2），aCOmParisonmatriⅩ（shownasequa−

Value〔入m。3−n）／（n−1）1Iti＄thene脚tiveBLVer乱ge

Go山orFocu皇：Tablel Comp乱risonScale
Intensityofirnportancel〕efinition

Crit打払：芯qu且Iimportancモ

ModerateimpoTtan⊂eEs台モnti且lor邑加OnglmpOrtanCeAl匝rn山iY亀：Demon＄tra．tedimportanee

Absolute importanceIntermediate valu闇between

Fig．2 工）ecomposlngOfAHP

adjacent judgment−2【oftheotherrootsofthecharacteristicspoZynomial

methodis used to do eva］uation鮎r quantita七iveofA．Thisvalueiseomparedwiththesameindex

factorsbaLSedonobjectivecosts，andforqualita，tive

obta主nedasanaver乱geOVera，1argen11mberofre− factorsbasedonsubjectivej11dgmentrespectivelyA
Ciprocalma七rieesofthe組meOrderwlmseentriesAndthenthemiddlepriDrit主esoftwotypefaetors
arer乱11dom．Thesati舐edvaltleOfCRis（：OnSidered

are caleulated．Finally，tlle COmprehensive evalu−

aBlessthanO．1intheexa血pleofthispa．per．

ation for the twomiddle priodtiesis done．The

hpart〔3），Pri0ritiesaresyntlle9izedbymuti−

plyinglocalprioritiesbythelmiorityoftheircor−

Weights to doit a．re derivedfrom孔nimportanceCOmparisonmatrixoveral1faJCtOrS．
Assumethattherea．rekqu叫titativefactorsa1l

respondingcriterioninthelevelabove，andaddingthemforea．chfactorina）evelaccordingtothecriーOfllfactors，SOthatthen11mberofqualitativef孔C−
torsi畠（nr−k）．Thealternat主venumberisdefined

ttさdait乱打ects．

Theextended AⅡP method proposedherein−

as m．The midd王e pri0rities ofqllantitative hc−

tegTateStlleeValu乱tionofquantitativefactorsandtor＄and q11alitativefactors a．redefined asfollows

q11alitativefaLetOr9intooneAtIPmodel．ItisbaBCd

TeSpeCtively：

onaviewthathrquantitativehctorsiti＄better
BLStOuSetheirobjectivecostsaBPOS＄ibletomal［e（3）evaluation，and for the ottlef fa．ctors use subjec・
tivej11dgment七ogetanapproximatere凱Ilt，finallyAIsoassumethatthehrmerkrows（orcolllmn）

a comprehensive evaluationis done basedon theinmatriⅩ（1）correspond畠tOquantitativefactors，

formerin七ermediatcr矧11ts，＄O thattIle aCCuraCy

andthelater（n−k）onescorrespondstoqualita−

of evaluation re5ultwillbeimproved．However， tivefaL：tOrB．TlleC】genVeCtOrwithre＄PeCt tO theit mllSt be noted that only by basing on a皿in−maximumeigenvalueofmatrix（1）areaLSfollows：

tegTatedcriterionforvariou＄触＝tOrSCanmakethe

巨1…

亡 叫1‥■ e几］r〔4）evaluationresl11tobjective乱mdreliahle．Theview
of亡OmPrehensiveevaluationwithq11antitativeand

qualitativefactorsisshowninFigure3・

Theaverageweightsofq11antitaitvefactorsaJld
qualitativefa／CtOr＄Can be obtainedfrom（4）andnoem且1iEjngthema月払llow5：

W叩αれ＝

∑≡1ei
∑た1e一＋∑ニ叫eu甲川】＝∑ニ叫1e（5）∑た1亡i＋∑こ仙ei

Fig．3 Comprehen昏iveevaluationprop
The魚nalpriorityofal1tllemalternatives，R＝Lrlr2，・・rml，wi11becalcul如edbymultiplyingthe

hthepartofdeeomposlngOftheextendedAHP

middleranksoftwokindsofhctorswiththeaver，
metllOd，thefactorsarecategorizedintotwotypes：
q11antitativefactors礼ndqtlalitativehctors．AIIP−3［

ageweightsoftwokindsoffactorsderivedby（5）：呈lM﹁■■■■−．⊥・・−Mれ

■−●m

叫叫

﹇2⁝

rl・⁚

rl巧

Stepl：AnalyEing the hiefBLrChy ofthe
example（郎ヱml

AccordingtotheaxiomofAIIP3・6）．wc酢t︼rthehierarchyofthisexampleshownasFigufe4．

Astheaverag亡Wei6htvectorofeomprehensive
evaluationis der主ved froln the comparison judg，TheformerthreefactorsareintangiblefaJ：tOrS，nomarketexi＄tthatcangivetheirco＄tValues．TIlermentoveral1hrtors，theweight写Oftwotypefac−
torssho111d befbaBibletothedeeisio】lm且ker，sini−
tiaユjudgmentwhichmadeoverallthcfactors．and

Other four hctors are qua．ntitative f肛tOr琴，theircost value can be calclllat．モ・d baBed on m乱rketin−

hrmation．

七heconsiBtentOffinalre畠ultcanbeguarallteed，、

Step2；Getti皿gCOmprellen8ive亡Omp且ri−
son m且trix

3．Anexample

InordertodocompreIlenSiveevaluation，anin−Iti露aneXampleth乱tuSeStheextendedAHP tegrated criterion foral1tlle hctorsis ne亡eSSary・
metlmd to applyin LCAwith quaJltita・tive andThe comprehensive comparison matrix is createdqualita七ivefactors・Instep3andstep41AⅡPis

acordingtothedecisionmakerspalrwisecompar−

usedtogetmiddleranksofalternativeswithqu乱n− isonjudgmeJltOfal1thefactors‥
Gさ9 9C57
肘75l

3l

3

15∧Jl

77／

1qU／

9ノ

ウリ

11−ヘリ1／5qJl

つJlll1つJ377■﹂リユ つd5 ノ／lP．51
クーリ

ウリ5−hUCOmPrehensivecompa∫i80nmatrixcreatedin

り3．′′′′

3l■hUl

vectorwithrespecttothemaxim11meigenvalueof

Pり1リリりりり〃l5

ウJ／／3′ノ

qualit乱tive臨ctors乱reCalculated fromtheeigen−3isdone．Theavera酢Weight50fquantitativeaAnd

15，aCOmprehensiveevaluationonthemiddlerulks0︒諾押押付⁝

titativeandqualitativef乱CtOrSre＄PeCtively・In阜tep

landstep2，TllePartOfquantitativt：PrOblemof Theconsisteneyindex（CI）ofthispairwisecom−

thisex且mpleis，eferedt。4）．

parisonmatrixisO．0947，andthecon＄istencyratio

Problモm

OfitisO．0717，theyareal1lessthanO・10，SOthat

Supposethattlledeci＄ionmakerwishestocllOOSe

WeCOnSiderthejudgmentofdecisionmal（eri写COn一

abestcaramongthreetypesaccordingt・07facT

由tencyroughly・tors（attributes）：OA（OutwardAppearance〕，NP（NoisePollution），GE（GaBeOu＄Emission）；PP（Pur−Step3：Eval11ating witb qⅦalitative h亡・tors

ehasePrice），MC（MaintenanceCostperyear），GC

Tlle pa．1rwise comparison matrices ofc乱r60n（GallonsperlO，000mi1esofcitydriving），GR〔Galv each qualitative criterion（OA，NP弧d GE）are
lonsperlO，000milesofruraldriving）・

Obtainedbyaquestionnairefordecision makeraBAdditionalcondition畠：hewillusethecarfor3 fo1lows：−4叫

1〔8）﹁■．．．■﹂

19E 丁・9G

79ノl ／

7 7

9 1／／11／91

criterion
19 1 9亡riterion N
9 1 1＄1．与0／gal−

11／91

﹈

亡riterion OAnr

mi1es・OVerthe3years；eXpeCted gaBOline costis

トyearsa．nddrive30，000citymilesa皿d20，000ruralchα：l馳at忙軋C即血血心nGENf■

且l仕ibll吐S

由比m鵬Y朗甜丑 ＼モー＼ノー打8H￠訂A伽且1ranlor血l駈mliY感

cⅣC ■て射A ca∫B ca∫亡Fig．4 Thehierarchyoftheexample
ヽThenormali21edeigenvector＄withregpecttothe

Therela．tpiveweigIltSOfaltcrn乱tiveson quanti−

maximumelgenValuesoftheabovethreematrice＄tativecriteriaPP，MC，GCandGRcanbegota月

are a5砧1lows．

払1low吉：c一山∋rion OA 亡riterion NP 亡riterioIIGE
0．81810．0909］・［呂；≡……書］（9）［ 0．09（】9criterion PP criterion MC critt！rion GC criterion GR甘Ajlldgment matrix ean be construCted fromthem．

From（7）weCangetthecomporisonmatriⅩOf

From（7）thepairwi＄eCOmPari別）nmatrixDfqual−叩姐titativefactors（PP，MC，GC，GR）鮎follows，
itativehctors（OA，NPandGE）isgotten・Itisa
itisasⅦbmatrixof（7）．
﹁■■■■■■L

7 1JnJrJ

7

ウリ1／l

■hリl

51．／／lEリ／

31ノ払1lows：

3l

ntリ

l

／︻リ

3

torwithrespecttoit＄maXimumelgenValuei＄aBl

subma七rixof（7）．AndtllenOrmalizedeigenvec−

0．30270，17310．93290．0904［…：壬；1什［芸三器ト［呂封〔10）TheimportanceofeachalternativeoIlqllanti−

Theimportanceofeachoptionis obtainedby

taitvefactors（0．2050，0．2995，0．49崩）isobtainedmu）tiplyingthematriⅩfbrmedbythcvectorsofop− bymultiplyingequation（12）byve血r（13）・Asa
tionweights（equation（9））bytheve⊂tOrOfcriteria

result，themiddlerankaboutqu乱ntitativefactors

Weights（equation（10））・Sothatthemiddelprior−

is出follows：Aノ／→月ノ／・→CJJ．

ityvectorabouttllequalitativefactorsis（0．6058，

Step5：Comprehensiveeval11ation

0．3122川．0糾9い・e・C′→月′→A′・

T九ecompre血enざ行ecompadsonmatrix（7）即七at step2isthebaBis ofcomprehenBiveevaLluation

Step4；Ev山uatingwitllq11且n七王tative血仁一Withqu且ntitativea皿dqualita．tivefactors．Because

tor邑

Relevantdataonthesequantita・tiveattributes tllatiti＄derived fromthecomp乱risonjudgnlent
OVeral1factors，tIlematrixisconsistentaboutboth

are known aE；below：
閉M250醐

G︒25︒認︒

8︒︒︒

B C2004︒600

A

ヽ■．■■∫

quantitativefa，CtOr＄andqualitative払ctors．Sothat

theresultoffinalevaluationdonebyitwi11bere−（11）

1iablc・Fromit we can get the eigenvectorwith

汀5一

re＄PeCttOthemaximlumelgenValueaBfollows．
From the above resultitis known t，hat the丘−

to・25660・69280・封610■11100朋270胴10・囲1］T

nalpriorityvectoraboutaJlthehctorsis：（0．5803．

（14）0．3093，0．1103），弧dthe丘n乱1r乱nkofthreecarsis：
Itrepresentstherela・tiveimportaJLCeSOfal1thefactorsincludingquantitativefactorsandqualita−
1ive fa￡tOr凱C→B→A，Thtis，COnSideringalLthe7factors，
the mostidealehoi（：eis car C．
Dis亡u6昌ion

Because the middle ranks got at step 3 andFigure4givesananalysisontheweightsofal1

Step4i畠abo11tq11alitativefactorsandquantitative

thefaLtOrSOVerall（wO），theweightsofqualitative

factors separately，the weightsthat tobe used to

faLCtOrS（wl）andtheweight畠Ofquantitativefactors

dothecomprehensiveevaluationshouldalsocorre−

inmiddleevaluatioIl（w2），theweightsoftwotype

SPOnd to quantitativefactorsandqualitativefac−

factor＄in comprehensive evaluation are pe＄ented

tor告TeSpe亡tivdy．Tberefore，We Choose the aveト inline Final．AELdFigure5expressthecompar−
aLgeSOfimport礼nCeSDfthetwokindsof臨ctorstoison ofpr）0rities oftllreealternatives decided bybecomprehensiveevaluationweights．

theweight5aboveindilferentlevels−eValuationof

Theaverageweightingwithrespecttoq11alita−

quantitativefa．ctor畠（quaL．），eValuationofqualita−

tive factor日iE；：0，4985．

tivefactors（qt！an・）andcomprehensiveevaluation
Oftwotypef肛tOrS（封几叫■i．e．0．49粥＝（0．2568十0．6928＋0．与461）／3；

Theaverageweightingwithresl）CCttOq11anti−
t乱tivefa￡tOrSis：0．1497．
i息軋14卯＝（0．1110＋0．0727＋0・3691＋0・0461）／4．

Normaユisingthem，WeCangetanaVerageWeight−
LngVeetOrWithrespecttoqu乱1itativef乱CtOrS andq11antitativehctor畠舶払1low畠：［呂：三…呂去】（15）

FromtIlemiddle−ranksofstep3alldstep4，theFig．5 Weig血tan乱Iy壷

middleevaluationresultmatrixcanbeconstruCted
各点砧uow畠．

Intheevaluationofqualita．tivefactors，themid−dle rankis；C→B→J4，and the priority dif，r16〕

鮎rencesbetweenthreecarsareもig．Intheev山一

Multiplyingthemiddleevaluationresultma七riコ亡uationofquantitative払cto指，themiddlerankis：

byt・heweightsofthetwokindsoffactor＄，WeCall jl・−＋B→C，andhavesInalldilrerence＄between

getthefinalrankofcomprehensiveevaluation．

three car＄．B11t the且naユ rankis：C → 月 →A，keepifLgthetrendofqualitativeevaluation．It

is the reBult ofefrectingfromthewcightsoftwo［ 呂；≡≡……≡割［3＝≡粧［呂；琵喜…］（17）ー6−key to ensure theextended AEP method be ob−

typefactorsincomI｝rChensiveevaluation・Andthis

weights（FinaE，Figure4）reflectedtheinicialjudg− jectiveand relia．bleis thecon弓istentofweightsof
mehtOVeral1thefactors（wO，Fig11re4）oftllede−comprehensiveevaluation．BecausethattIleaVer，

age weight vectorofcomprehensive evaluationis

cisiollm止er．

derivedfromtlleCOmParisonjudgmentoveral）fac−
tor＄，theconsistelltOffinalre＄ult canbe guaran−

teed．TheextendedAHPmethodhasadvantagesof
simplicity，鮎xibility，intuitiveappeal，andtheabil−
itytointegra．teqllantitativeal14qualitativefactt｝rS．

in ont！mOdel．

参考文献
1）Ⅴ山ationofLifeCycleInventorie＄＝ACom−parisonofThreeMethodologies，MaterialSys−

Fig．6 Prioritycomparison

temsLaboratory，MIT，December31，（1993）
2）「環境負荷評価に関する内外動向調査」，株

4． Con亡1u．sion

式会社日本総合研究軌】弧．〔19鮎）In the pa虐tl与ycar＄，AtIP haB been applied

3）T・L・Saaty＝ Concepts，Theory，and Tech−

tomanyfieldssuccessfully，ALthoughitha＄＄Omeniques：Ra皿k Generation，Preservation，and

畠hortcomings，AHP has been accepted a5a＄lg−

Reversalillthe Analytic Hierarchy Decisiofl

nifieantcontributiontothe5tudyofmulticriteria

Proces阜，Decision Science，Vol．18，PP．1与7

decisionmaking．ItcansoIvenotonlyintangible

177，1987

problemsbutalsogivethedifferencedegreeofthe
4）T．L．Sa且ty，L・G・VaJga占，R・E−W由dell：As一prioritiesofalternativesint11itively・

馬essingAttributeWeight畠byR且tios，OMEGA

MulticriteriadecisionmakinglnaCtllalisavery

TheIIlt．JiofMgmtSci．，Vol・11，No・1，pP・

COmplieated problem．They arealmo＄tincluded

9【13，（198封withbothq11antitativeaLndq11alitativefactorssim11−
t乱nO11Sely．Inordertoensuretheevaluationtobe5〕R・R乱manathan and L・S・Gameshニ Ene柑ydoneobjectivelyandreliability，tllelluma110Plnion

Re＄OurCe AllocationIncorporating Qualita−

must be con＄idered to tarticipatein the decision

tiveandQuantitativeCriteI・ia：AnIntegrated

makingprocess・Forthesakeofimprovlngtheae−

ModelUsing GoalProgrammln苫and AHP，

CuraCy andreliabilityoftheevaluationrestllts，itSocio−Ecom．Plann．Sci．，Vol．29，No．3，pp．

is necessarythatrforquantitativefartorsa占11Slng

197−218，（1995）

theirobjeetivecostsaBpOBBibletodoevaluation，

6）T・L・Saaty：Analytic HierarchyAnalysis，

andforqualitative一礼CtOrStOuSeh11man ssubjec−

McGraw−Hi11，Pp・与4，（1980）

tivejlldgmentstogetanapproximateresult・The
一7−・