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16
EdytaAbramek,TomaszWachowicz
TOPSIS
TOPSIS[HwYo81]isbasedonmeasuringdistancestothepositiveideal
andnegativeidealsolutions.Themethodusesthesameadditiveaggregation
andassumestheutilitycompensationsimilarlytotheASM.However,the
TOPSISalgorithmissimplerthanASMandrequiresfromDMassigning
thecriteriaweightsonly.Ontheotherhand,TOPSISdoesnotmeasureDM’s
preferencesprecisely,theutilityscoresofthecriteriaoptionsarereplacedwith
statisticaldistancemeasure,butitmakesthismethodmore“objective”than
theAMS.TOPSISalgorithmrequires:
1.Buildingthenormalizeddecisionmatrix.Normalizedvectorsofxjkbuild
thenormalizeddecisionmatrixN.
2.Computingtheweightednormalizeddecisionmatrix.TheelementsofN
aremultipliedbythecriteriaweightswk.Aweightednormalizedperform-
ances(vjk)aredetermined.
3.Determiningthepositiveideal(A+)andnegativeideal(A–)solutions:
A
+=
(
v
1
+
,
v
2
+
,
K
,
v
n
+
),
where
v=
k
+
max
j
(
v
jk
),
A
−=
(
v
1
−
,
v
2
−
,
K
,
v
n
−
),
where
v=
k
−
min
j
(
v
jk
).
(4)
(5)
4.Calculatingtheseparationmeasures(distances)foreachalternativejfrom
PIS(
d)andNIS(
+
j
d)respectively.
−
j
5.Determiningtherelativeclosenessofeachalternativetotheidealsolution:
S
j
=
d
j
+
d
+
−
j
d
−
j
,
forj=1,2,…,m.
where
0
≤
S
j
≤
1
.
Thecloserthealternative
atoPIS,thelargerthevalueof
j
S
j
.
6.Rankingthealternativesindescendingorderusing
S
j
.
(6)
