Page 321 - Materials Chemistry, Second Edition

320 15. Barriers identification and prioritization

Substep 3: Determining the fuzzy optimum weights.
The fuzzy optimum weights (relative influences) of the four influential factors including
T 1 ,EC 2 ,SM 1 , and SM 2 on T 2 are determined by solving the following programming (15.22).
minξ ∗
s:t:
T 2 ,L T 2 ,M T 2 ,U
ω ω ω
T 1 3 ∗ T 1 ∗ T 1 ξ ∗
5
T 2 ,U ξ , T 2 ,M 2 ξ T 2 ,L
ω ω ω
2 2
EC 3 EC 3 EC 3
T 2 ,L T 2 ,M T 2 ,U
ω ω ω
9
T 1 7 ∗ T 1 ∗ T 1 ξ ∗
T 2 ,U ξ , T 2 ,M 4 ξ T 2 ,L
ω 2 ω ω 2
SM 1 SM 1 SM 1
T 2 ,L T 2 ,M T 2 ,U
ω ω ω
7
T 1 5 ∗ T 1 ∗ T 1 ξ ∗
T 2 ,U ξ , T 2 ,M 3 ξ T 2 ,L
ω 2 ω ω 2
SM 2 SM 2 SM 2
T 2 ,L T 2 ,M T 2 ,U (15.22)
ω ω ω
EC 3 5 ∗ EC 3 ∗ EC 3 ξ ∗
7
T 2 ,U ξ , T 2 ,M 3 ξ , T 2 ,L
ω ω ω
2 2
SM 1 SM 1 SM 1
T 2 ,L T 2 ,M T 2 ,U
ω ω ω
5
SM 2 3 ∗ SM 2 ∗ SM 2 ξ ∗
T 2 ,U ξ , T 2 ,M 2 ξ , T 2 ,L
ω ω ω
2 2
SM 1 SM 1 SM 1
ω T 2 ,L +4ω T 2 ,M + ω T 2 ,U
X
k k k ¼ 1
6
k¼T 1,EC 3,SM 1,SM 2
ω T 2 ,L ω T 2 ,M ω T 2 ,U
k k k k ¼ T 1 ,EC 3 ,SM 1 ,SM 2
ω T 2 ,L 0 k ¼ T 1 ,EC 3 ,SM 1 ,SM 2
k
∗
The results are presented in Table 15.5. The optimum value of ξ is 0.4074.
Substep 4: Defuzzying the fuzzy weights into crisp weights.
The defuzzied weights (the relative influences) of these four influential factors can be de-
termined as presented in Eqs. (15.23)–(15.26).
0:4385 + 4 0:4385 + 0:4914
T 2
ω ¼ ¼ 0:4473 (15.23)
T 1 6
TABLE 15.5 The relative influences of T 1 ,EC 2 ,SM 1 , and SM 2 on T 2 .
T 2 , L T 2 , M T 2 , U
ω k ω k ω k
k¼T 1 0.4385 0.4385 0.4914
k¼EC 3 0.2348 0.2753 0.3101
k¼SM 1 0.1001 0.1053 0.1122
k¼SM 2 0.1511 0.1689 0.2096