Page 52 - Decision Making Applications in Modern Power Systems

Multicriteria decision-making methodologies Chapter | 1 27

TABLE 1.8 Fuzzy triangular scale for equivalent Saaty scale [87 92].
Definition Saaty scale Fuzzy triangular scale
Equally important 1 1,1,1
Weakly important 3 2,3,4
Fairly important 5 4,5,6
Strongly important 7 6,7,8
Absolutely important 9 9,9,9
The values between two adjacent scales 2 1,2,3
4 3,4,5
6 5,6,7
8 7,8,9

Step 5: Calculation of fuzzy weight
The weight is calculated by the following formulae:

21
ð
W i 5 G i 3 G 1 1G 2 1 ... 1G n Þ ð1:38Þ
ðÞ; ðÞ; ðÞ
W i 5 xG i yG i zG i ð1:39Þ
where x, y, and z are the three values of the triangular membership
function.
Step 6: Defuzzification and normalization
The values determined in Step 5 are converted based on the center of
area. Let the defuzzified value be D i :

ðÞ
ðÞ
ðÞ
xG i 1 yG i 1 zG i
D i 5 ð1:40Þ
3
The value is normalized by the following equation:
D i
N i 5 ð1:41Þ
m
P
D i
k51
The alternatives with the highest value of N i are the most preferred ones
and are suggested by the decision makers.