Page 186 - Materials Chemistry, Second Edition

184 9. Life cycle decision support framework: Method and case study

TABLE 9.3 Transformation rules for Z-number linguistic variables to fuzzy
numbers (Aboutorab et al., 2018).
Linguistic terms Membership function
(EI,VL) (1, 1, 1)
(EI,L) (1, 1, 1)
(EI,M) (1, 1, 1)
(EI,H) (1, 1, 1)
(EI,VH) (1, 1, 1)
(WI,VL) (0.21, 0.32, 0.47)
(WI,L) (0.37, 0.55, 0.82)
(WI,M) (0.47, 0.71, 0.82)
(WI,H) (0.56, 0.84, 1.26)
(WI,VH) (0.63, 0.95, 1.43)
(FI,VL) (0.47, 0.63, 0.79)
(FI,L) (0.82, 1.10, 1.37)
(FI,M) (1.07, 1.42, 1.78)
(FI,H) (1.26, 1.68, 2.10)
(FI,VH) (1.43, 1.90, 2.38)
(VI,VL) (0.79, 0.95, 1.11)
(VI,L) (1.37, 1.64, 1.92)
(VI,M) (1.78, 2.13, 2.49)
(VI,H) (2.10, 2.52, 2.94)
(VI,VH) (2.38, 2.85, 3.33)
(AI,VL) (1.11, 1.26, 1.42)
(AI,L) (1.92, 2.19, 2.47)
(AI,M) (2.49, 2.84, 3.20)
(AI,H) (2.94, 3.36, 3.78)
(AI,VH) (3.33, 3.80, 4.28)

between pairwise comparison data and the calculated weights based on the opinion of the kth
stakeholder; and i¼1, 2, …, m, j¼1, 2, …, n, and k¼1, 2, …, p.
The fuzzy weights obtained from Eq.(9.3) can be defuzzied into crisp weight by Eq. (9.4).

l j +4∗m j + u j
w j ¼ (9.4)
6
where, j¼1, 2, …, n represents the jth criterion.