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CHOSENMETHODSANDTECHNIQES…
17
PROMETHEEII
PROMETHEEII[BVMa86,p.228-238]appliesthefunction
f
ia
(
n
)
that
returnstheperformanceofalternative
aforcriterioni.Comparingtwoalter-
n
natives
a
m
and
a
n
intermsofcriterioniwedeterminethedifference
δ
i
(
a
m
,
a
n
)
=
f
i
(
a
m
)
−
f
i
(
a
n
)
,whichiscomparedwithpreference
(pand
)
indifference
(qthresholdsandusedlaterforbuildingtherankingofalterna-
)
tives.Therankingprocedurerequires:
1.Determiningthedifferences
δ
k
(
a
i
,
a
j
)
foreachpairofalternativesfrom
setAandforeachcriterionkrespectively.
2.Determiningthevaluesofthepreferencefunctions
P
k
(
a
i
,
a
j
)
foreach
criterionseparately.Thepreferencefunctionassignstoeachdifference
δ
k
(
a
i
,
a
j
)
avaluefromtherange
[]
0,whichreflectsthenegotiator’s
;
1
strengthofpreference.Sixdifferenttypesofthepreferencefunction
aresuggested[BVMa86,p.228-238],e.g.,
P(
δ
i
)
=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
δ
p
0
1
−
−
q
q
q
δ
<
δ
δ
>
≤
≤
q
p
p
3.Calculatingtheoverallpreferenceindexes:
Π
(
a
i
a
j
)
=
∑
k
w
k
P
k
(
a
i
,
a
j
)
,
,
Π
(
a
j
a
i
)
=
∑
k
w
k
P
k
(
a
j
,
a
i
)
.
,
4.Identifyingtheleavingandenteringflowforeachalternative:
Φ
+
()
a
i
=
m
1
−
1
i
∑
j
m
≠
=
1
j
Π
(
a
i
,
a
j
)
,
Φ
−
()
a
i
=
m
1
−
1
i
∑
j
m
≠
=
1
j
Π
(
a
j
,
a
i
)
.
(7)
(8)
(9)
(10)
(11)
