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18
EdytaAbramek,TomaszWachowicz
5.Determinationofthepreferencenetflowforeachnegotiationofferaccord-
ingtotheformula:
Φ
()
a
i
=
Φ
+
()
a
i
−
Φ
−
()
a
j
.
(1)
6.Buildingtherankingoftheoffersaccordingtodecreasingvalueofpre-
ferencenetflowΦ.
PROMETHEEdoesnotrequiremanytiresomeassignmentsandcalcula-
tions.Howeverthedefinitionofthepreferencethresholdmaybeunintuitivefor
DM.ThebiggestdisadvantageofPROMETHEEistherankingreversalprob-
lem,whichistypicalforthemethodsthatbaseonthepair-wisecomparisons
[KePe96,p.457-461].
AHP
AHP[Saat80]isanotherpair-wisecomparison-basedmethod.Itde-
composestheproblemintoatomicelementsatthevariouslevelsoftheproblem
hierarchythatareeasytoevaluatebyDM.TheDMneedsonlytodecideifone
oftheelementfromthepairismorepreferredthananotherornot.Itmakes
itsdecisionusingthe9-pointverbalscale.ThemajoradvantageofAHPisthat
itdoesnotrequirefromDMassigningscorestotheattributesandoptions
directly,butthescoresarederivedfromDMpair-wiseevaluation.Ontheother
hand,ifthedecisionproblemisbigitsdecompositionmaycausehundreds
pairs,theevaluationofwhichwouldbetiresomeorevenimpossibletoDM.
AHPisalsosensitive,similarlytoPORMETHEE,totherankingreversalprob-
lem.
IngeneraltheAHPprocedurerequirescomparingallmalternativeswith
respecttoeachcriterionjseparatelyandbuildingthecomparisonmatrices
B
j
suchas:
B
j
=
⎡
⎢
⎢
⎢
⎢
⎣
w
w
w
1
2
n
j
j
j
M
/
/
/
w
w
w
1
1
1
j
j
j
w
w
w
1
2
n
j
j
j
/
/
/
w
w
w
2
2
2
j
j
j
L
L
w
w
1
2
j
j
/
/
w
w
n
n
j
j
⎤
⎥
⎥
M
O
w
n
j
/
w
n
j
⎥
⎥
⎦
(13)
Eachelement
w/
a
j
w
b
j
describestheimportanceofalternativeacom-
paredwithalternativebforcriterionj,where
w
a
j
and
w
b
j
aretheweight
ofthealternativesaandbrespectively.Tofindthevectorofweightsw
jforall
thealternativeswemayusethefollowingformula:
