Page 301 - Materials Chemistry, Second Edition

300 14. LCS prioritization of energy storage under uncertainties

TABLE 14.2 Transformation rules of linguistic variables of decision-
maker.
Linguistic terms Membership function
Very low(VL) (0,0,0.2)
Low (L) (0,0.2,0.4)
Good (G) (0.3,0.5,0.7)
High (H) (0.6,0.8,1)
Very High (VH) (0.8,1,1)

L M R
decision-maker D j for criteria C k . Then, the aggregate fuzzy linguistic rating a ik ¼ a , a , a
ik ik ik
for criteria C k of alternative A i can be calculated by:

a ik ¼ 1=rð Þ
a ik1 ⋯ a ikj ⋯ a ikr (14.14)
a L a M a R
L P r ikj M P r ikj R P r ikj
where a ¼ , a ¼ , and a ¼ .
ik j¼1 r ik j¼1 r ik j¼1 r
Step 2: Determine the weights of all the criteria. In this chapter, the criteria weights
(w 1 ,w 2 ,⋯,w n )of sustainability ranking for different electrochemical energy storage technolo-
gies from the perspective of life cycle is determined using the Bayesian best-worst
method (BBWM).
Step 3: Build the initial fuzzy decision matrix. The initial fuzzy decision matrix A, as shown
in Eq. (14.15), can be obtained based on Step 1, and the entries are given in the form of a tri-
angular fuzzy number.

⋯
2 3 2 L M R L M R L M R 3
a 11 a 12 ⋯ a 1n a , a , a 11 a , a , a 12 a , a , a 1n
12
1n
1n
12
11
11
6 7 6 L M R L M R ⋯ L M R 7
a 21 a 22 ⋯ a 2n a , a , a a , a , a a , a , a
6 7 6 21 21 21 22 22 22 2n 2n 2n 7
A ¼ a ik ¼ 6 7 ¼ 6 7
m n 6 ⋮ ⋮ ⋮ 7 6 ⋮ ⋮ ⋮ ⋮ 7
4 ⋮ 5 4 5
L
L
M
L
M
M
a , a , a R a , a , a R ⋯ a , a , a R
a m1 a m2 ⋯ a mn m1 m1 m1 m2 m2 m2 mn mn mn
(14.15)
Step 4: Normalize the initial fuzzy decision matrix. The criteria hold different attributes,
including benefit-type attribute (the larger the better) and cost-type attribute (the smaller the
better). Therefore, the normalization processing on all criteria need to be performed first.
For benefit-type criteria, the normalization processing is expressed as Eq. (14.16):

L M R
b ik ¼ a =t k , a =t k , a =t k (14.16)
ik ik ik
R
where t k ¼ max a ik
i
For cost-type criteria, the normalization processing is expressed as Eq. (14.17):
R M L
b ik ¼ t k =a , t k =a , t k =a (14.17)
ik ik ik
L
where t k ¼ min a ik .
i