Page 276 - Materials Chemistry, Second Edition

274 13. Multi-criteria decision-making after life cycle sustainability assessment under hybrid information

Eqs. (13.13), (13.14), the average intuitionistic fuzzy score of the ith alternative with respect to
the j-th criterion can be determined by Eq. (13.15).

K
X k K
A k k k 0 1
ij μ , υ , π ij K K K K
ij
ij
k¼1 k¼1 Y 1 μ k Y k Y 1 μ k Y υ
@ , υ , k A (13.15)
K K
x ij ¼ ¼ ¼ 1 ij ij ij ij
k¼1 j¼1 j¼1 j¼1
where x ij represents the average intuitionistic fuzzy score of the ith alternative with respect to
the jth criterion.
Step 4: Transforming the average intuitionistic fuzzy score into the interval number. The
average intuitionistic fuzzy score is transformed into the interval number according to
Eq. (13.11), as presented in Eq. (13.16).
K K
" #
Y
h L U i k Y k
x ¼ x ij x ij ¼ 1 1 μ ij 1 υ ij (13.16)

ij
k¼1 j¼1
where x ij , which is an interval number, represents the average performance of the ith alter-

native with respect to the jth criterion based on the opinions of the K groups of stakeholders,
L
U
x ij and x ij are the lower and upper bounds of the interval number x ij , respectively.

13.2.2 Multi-criteria decision analysis under multi-data condition
The multi-criteria decision analysis model can be described as follows:
(1) There are a total of M alternative industrial or energy systems, and they are {S 1 ,S 2 ,…,S M };
(2) There are N criteria in environmental, economic, and social dimensions for sustainability
assessment of the alternative industrial or energy systems, and they are {C 1 ,C 2 ,…,C N }; and
(3) The weights of the N criteria for sustainability assessment are {ω 1 ,ω 2 ,…,ω N }, and they can
represent the relative importance of these criteria in the decision-making process and the
preferences of the stakeholders.

The framework of the developed multicriteria decision analysis for life cycle sustainability
ranking of energy and industrial systems is presented in Fig. 13.1.
The multi-criteria decision analysis under multi-data condition developed in this study is
specified as follows:
Step 1: Determining the decision-making matrix. The decision-making matrix consists of
all the alternatives (i.e., alternative energy or industrial systems), the criteria for evaluating or
prioritizing the alternatives, and the data of the alternatives with respect to each of the eval-
uation criteria. As for the data with respect to the “hard” criteria, they can be described by
using the real numbers or the interval numbers directly. As for the data with respect to
the “soft” criteria, they can be determined by using the eleven linguistic variables; subse-
quently, these linguistic variables can be transformed into intuitionistic fuzzy numbers; then,
these intuitionistic fuzzy numbers can be aggregated and averaged into the average
intuitionistic fuzzy scores by Eq. (13.15); and finally, the average intuitionistic fuzzy scores