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component utilities and weights and the performance of the entered uncertain alternatives
to definitely reject poor alternatives, mainly by discarding dominated and/or non-
potentially optimal alternatives.
The GMAA system computes the potentially optimal alternatives among the non-dominated
alternatives because these are alternatives that are best ranked for at least one combination
of the imprecise parameters, i.e., weights, component utility functions and alternative
performances.
Finally, Monte Carlo simulation techniques enable simultaneous changes of the weights and
generate results that can be easily analyzed statistically to provide more insight into the
multi-attribute model recommendations (Mateos el at, 2006). While the simulation is
running, the system computes several statistics about the rankings of each alternative, like
mode, minimum, maximum, mean, standard deviation and the 25th, 50th and 75th
percentiles. This information can be useful for discarding some available alternatives, aided
by a display that presents a multiple boxplot for the alternatives.
The GMAA system provides three general classes of simulation. In the random weights
option, weights for the attributes are generated completely at random, which means that
there is no knowledge whatsoever of the relative importance of the attributes. In the rank
order weights option, attribute weights are randomly generated preserving a total or partial
attribute rank order, which places substantial restrictions on the domain of possible weights
that are consistent with the DM's judgement of criteria importance, leading to more
meaningful results. Finally, in the response distribution weights option, attribute weights are
now randomly assigned values taking into account the normalized attribute weight
intervals provided by the DM in the weight elicitation methods.
The Universidad Politécnica de Madrid registered the GMAA system and a free version
(installation package and user's guide) is available for academic purposes at
http://www.dia.fi.upm.es/~ajimenez/GMAA.
3. Real application to complex decision-making problems
GMAA has proved to be useful for solving complex decision-making problems in different
areas. We summarize below some of the problems in which GMAA was used as a key part
of the decision-making process.
3.1 Selection of intervention strategies for the restoration of aquatic ecosystems
contaminated by radionuclides
The first problem in which the GMMA system was used was to evaluate intervention
strategies for the restoration of aquatic ecosystems contaminated by radionuclides.
This problem was studied in depth as part of several European projects in which we
participated: MOIRA (A model-based computerized system for management support to
identify optimal remedial strategies for restoring radionuclide contaminated aquatic
ecosystem and drainage areas) (Monte et al., 2000), COMETES (implementing computerized
methodologies to evaluate the effectiveness of countermeasures for restoring radionuclide
contaminated freshwater ecosystems) (Monte et al., 2002), EVANET-HYDRA (evaluation
and network of EC-decision support systems in the field of hydrological dispersion models
and of aquatic radioecological research), and EURANOS (European approach to nuclear and
radiological emergency management and rehabilitation strategies).
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