Page 44 - Decision Making Applications in Modern Power Systems

Multicriteria decision-making methodologies Chapter | 1 21

TABLE 1.5 Transfer function for PROMETHE [61,65,66].
Preference functions
Sl. no. Name or type of Graphical representation Mathematical representation
creation
1 Usual P(d )
j
1 0if d j # 0
PðdÞ j 5
1if d j . 0
j d
2 Quasi P(d )
j
1

0if d j # q j
PðdÞ j 5
1if d j . q j
j q j d
3 Linear P(d ) 2 d j 3
j if d j # q j
1 6 6 p j 7
7
7
PðdÞ j 5 6
0if d # 0
4 5
1if d j . q j
j p j d
4 Step or level P(d )
j
1
2 3
0if d j , q j
PðdÞ j 5 0:5if q j , d j # p j 5
4
1if d j . q j
j q j p
5 Indifference P(d ) j
1 2 0if d j # p j 3
d j 2 q j
6 7
6 if q j , d j # p j 7
p j 2 q j
PðdÞ j 5 6 7
4 5
j q j p j d 1if d j . q j
6 Gaussian P(d )
j
2d 2 3
2
j
2σ 2
1 PdðÞ j 5 4 6 1 2 e j 7 5
0if d # 0
j σ j d
and
1 X
2
F aðÞ 5 5 gp x; aÞ ð1:32Þ
ð
m 2 1
xAA
where m is the possible number of decisions.