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Multicriteria decision-making methodologies Chapter | 1 17

Step 6: Calculation of the aggregate dominance matrix (ADM)
The elements of the ADM are calculated as the product of concor-
dance and discordance indexes and threshold values (cd kl and dd kl ).

ADM kl 5 cd kl 3 dd kl ð1:27Þ
Step 7: Preference ordering based on the value of the ADM
The best alternatives will be the one that dominates all the other alterna-
tives. The dominance is determined based on the presence of “1.” If any of
the value in a column is equal to 1, it can be stated that the column with “1”
is preferred over the corresponding row.
The ELECTRE is preferred over the other method as it can deal with the
heterogeneous scales. The drawbacks of this method are related to its versa-
tility, and it needs a very good understanding of the objective a decision
maker is working with, especially for quantitative features. Few applications
of ELECTRE in energy planning are given in Table 1.3.

1.2.6 Preference ranking organization method for enrichment
evaluation

PROMETHE was developed by Brans et al. [61]. This method is dominantly
utilized in the field of risk and structural analysis, and mining engineering.
This method encompasses a group level involvement in the decision-making.
It also deals with both qualitative and quantitative information. In this
method, there are various categories of analysis in this method, and each of
them is named as versions—PROMETHE I, PROMETHE II, PROMETHE
III, PROMETHE IV, PROMETHE V, and PROMETHE VI. The type of
analysis the method focuses on is given in Table 1.4 [61 64].
This method involves the selection of transfer function and fixing the
value of threshold. The transfer function, also called preference, is given in
Table 1.5 [61,65,66].
PROMETHE II is the most commonly used method to calculate the rank
of various alternatives. The flowchart of the process for PROMETHE is
given in Fig. 1.4. The steps that are described later have been followed while
calculating the rank of the alternatives.
Step 1: Calculation of preference degree
To start with, a decision matrix with rows filled with alternatives and col-
umns with criterion is prepared. This is followed by giving weights to the
entire criterion and establishing the threshold values. The transfer function is
also selected for each criterion. Let c i aðÞ and c i bðÞ be the value of criterion j
for decisions a and b. The difference d i a; bð Þ is calculated between the values
given in the following equation: