Page 297 - Materials Chemistry, Second Edition

296 14. LCS prioritization of energy storage under uncertainties

multiple decision-makers, the BWM will use the average operator (such as arithmetic or geo-
metric mean) to aggregate the preferences of multiple decision-makers and calculate the ar-
ithmetic mean of the criteria weights obtained from the individual decision-makers, which
has the disadvantages of outlier sensitivity and restricted information provision. Actually,
different decision-makers maybe select different best criteria and worst criteria when using
BWM to determine the criteria weights. So, the BWM needs to be extended to the group
decision-making environment. In 2019, the Bayesian best-worst method (BBWM) was pro-
posed by Mohammadi and Rezaei (2019), which can determine the aggregated criteria
weights for a group of decision-makers at once, other than the average operator. The inputs
between BWM and BBWM are same, but the outputs of BBWM is the optimal aggregated
weights, which can consider the total preferences of all decision-makers or stakeholders along
with the confidence level for ranking the criteria.

14.3.2.1 The basic theory and step of BWM
The BWM determine the criteria weights by pairwise comparisons between the best criteria
and other criteria as well as between the worst criteria and other criteria conducted by only
one decision-maker. The detailed theory and steps of BWM are listed as follows (Guo and
Zhao, 2017; Rezaei, 2015; Rezaei, 2016).
Step 1: The decision criteria system needs to be built, which consists of a set of decision
criteria. The criteria values can represent the overall performances of different alternatives.
Suppose there are n criteria {c 1 ,c 2 ,⋯,c n }.
Step 2: The best criterion c B and the worst criterion c W are identified by decision-makers in
this step. The best criterion is the most desirable or the most important based on the prefer-
ences of decision-makers, while the worst criterion is the least desirable or the least important
criterion among all the criteria based on decision-makers’ preferences.
Step 3: The pairwise comparison between the best criterion and other criteria is conducted
in this step. The decision-makers calibrate their preferences of the best criterion to other
criteria using a number from one to nine, where one indicates the best criterion is equally im-
portant to the compared criterion, and nine means the best criterion is extremely more impor-
tant to the compared criterion. Based on the pairwise comparisons between the best criterion
and other criteria, the “best-to-others” vector A B can be obtained as:

ð
A B ¼ a B1 , a B2 , ⋯, a Bn Þ (14.1)
where a Bj represents the preference of the best criterion to the criterion c j .
Step 4: The pairwise comparison between the worst criterion and other criteria is
conducted in this step. The decision-makers calibrate their preferences of other criteria to
the worst criterion using a number from one to nine. Based on the pairwise comparisons be-
tween other criteria and the worst criterion, the “others-to-worst” vector A W can be obtained
as:

A W ¼ a W1 , a W2 , ⋯, a Wn Þ (14.2)
ð
where a jW represents the preference of the criterion c j over the best criterion.
∗ ∗ ∗
Step 5: The optimal weights (w 1 ,w 2 ,⋯,w n )of all the criteria can be obtained in this step.
According to the rules that the weight vector must be in the neighborhood of the equations