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 265

(if necessary); 3) quantifying preferences (which includes the assessment of the component
attribute utilities, as well as the weights representing the relative importance of criteria); and
4) evaluating alternatives and performing sensitivity analysis (SA).
The GMAA system accounts for uncertainty about the alternative performances.
Quantifying preferences involves assessing component utilities, which represent the DM's
preferences over the possible attribute performances, and eliciting weights, which account
for the relative importance of criteria.
The GMAA system provides four procedures for assessing component utilities: 1) construct
a piecewise linear imprecise utility function, 2) construct an imprecise utility function with a
gamble-based method (Jiménez et al., 2003), 3) assign imprecise utilities to discrete attribute
values and 4) directly provide subjective values.
There are two main ways of representing the relative importance of criteria. The first is to
preemptive order attributes (Adelbratt & Montgomery, 1980), and the second is to use
attribute weights. The second option is more widespread and is used in the GMAA system.
Different methods have been proposed to elicit weights by different authors, such as
DIRECT point allocation , simple multi-attribute rating technique - SMART - (Edwards, 1977),
SWING weighting (von Winterfeldt & Edwards, 1986; Edwards & Barron, 1994), SMART
using swings - SMARTS - (Edwards & Barron, 1994), SMART exploiting ranks - SMARTER -
Edwards & Barron, 1994), TRADE-OFFS weighting (Keeney & Raiffa, 1993), pricing out method
(Keeney & Raiffa, 1993), analytic hierarchy process -AHP- (Saaty, 1980), or preference
programming (Salo & Hämäläinen, 1995). The GMAA system provides DIRECT point
allocation and TRADE-OFFS weighting .
The GMAA system accounts for incomplete information about the DM's preferences
through value intervals as responses to the probability questions that the DM is asked,
leading to classes of utility functions and weight intervals. This is less demanding for a
single DM and also makes the system suitable for group decision support, where individual
conflicting views in a group of DMs can be captured through imprecise answers.
An additive multi-attribute utility function is used to evaluate the alternatives, taking the
form

n


u ( S j )  w i u i ( x i j ) (1)

i  1

where w i is the i th attribute weight, x i is the performance for alternative S j in the i th attribute
and u i ( x ij ) is the utility associated with the above performance.
For the reasons described in (Raiffa, 1982; Sterwart, 1996), the additive model is considered
to be a valid approach in most practical situations. It is used to assess, on the one hand,
average overall utilities, on which the ranking of alternatives is based and, on the other,
minimum and maximum overall utilities, which give further insight into the robustness of
this ranking.
The GMAA provides several types of SA. It can assess the stability weight interval for any
objective at any level in the hierarchy. This represents the interval where the average
normalized weight for the considered objective can vary without affecting the overall
ranking of alternatives or just the best ranked alternative.
On the other hand, the assessment of non-dominated and potentially optimal alternatives (Mateos
et al., 2007) takes advantage of the imprecise information gathered during the assignment of