GMAA: A DSS Based on the Decision Analysis Methodology - Application Survey and Further Developments - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 281

second approach, denoted AP2 (Ahn and Park 2), alternatives are ranked according to the
difference between the dominating measure  k and a dominated measure

m

   D ,

k lk

l  1, l k

i.e., on the basis of  k -  k .
Two new dominance measuring methods were proposed in (Mateos et al, 2011a). The first
one, denoted DME1 (Dominance Measuring Extension 1), is based on the same idea as Ahn
and Park suggested. First, dominating and dominated measures are computed from the paired
dominance values and then a net dominance is derived. This net dominance is used as a
measure of the strength of preference. DME1 computes the positive and negative
dominating measures and positive and negative dominated measures. They are used to
compute first a proportion representing how strongly one alternative is preferred to the
others and second a proportion representing how intensely one alternative is not preferred
to the others. Finally, DME1 subtracts both proportions to compute the intensity of the
preference. DME1 can be implemented as follows:
1.

Get the paired dominance values D kl and the dominance matrix D as in (2).

2. Compute the dominating measures α k , α k + and α k - for each alternative A k :

m m m

 

  

  D ,   D ,   D

k kl k kl k kl

l  1, lk l   1, lkD , 0 l   1, lkD , 0

kl kl

3. Compute the proportion




 

P 

k

 .

k

 



k k

4. Compute the dominated measures β k , β k + and β k - for each alternative A k :

m m m

 

  

  D ,   D ,   D

k lk k lk k lk

l  1, l k l   1, l kD , 0 l   1, l kD , 0

lk lk

5. Compute the proportion




 

P 

k

 .

k

 



k k

 
 
7. Rank alternatives according to the P k values, where the best (rank 1) is the alternative
for which P k is a maximum and the worst (rank m ) is the alternative for which P k is the
minimum.
The drawback of the DME1 method is that when the dominance matrix D contains all
negative elements, i.e., when all the alternatives are non-dominated, the algorithm is unable
to rank the alternatives because they are all equal to 0.
In the second method, denoted DME2 (Dominance Measuring Extension 2), alternatives are
ranked on the basis of a preference intensity measure . Paired dominance values are first
transformed into preference intensities PI kl (step 2) depending on the preference among

6.

PP Pk , ,..., m .

Calculate the preference intensity value P k for each A k :

k k

k