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involve imprecise information. Several reasons are given in the literature to justify why a
DM may wish to provide incomplete information (Weber, 1987; Sarabando & Dias, 2010).
For instance, regarding alternative performances, some parameters of the model may be
intangible or non-monetary as they reflect social or environmental impacts. Also, the
performances may be taken from statistics or measurements, and the information that
would set the value of some parameters may be incomplete, not credible, contradictory or
controversial. At the same time, it is often not easy to elicit precise weights, which may be
represented by intervals, probability distributions and even fuzzy values, or just satisfying
ordinal relations. DMs may find it difficult to compare criteria or not want to reveal their
preferences in public. Furthermore, the decision may be taken within a group, where the
imprecision of the preferences is the result of a negotiation process.
This situation where it is not possible to indicate precise values for the parameters and
quantities involved is often referred to as
decision-making with imprecise information
,
with
incomplete information
or
with partial information
, together with
incomplete knowledge
or
linear
partial information
(Kmietowicz & Pearman, 1984; Kirkwood & Sarin, 1985; Hazen, 1986; Ríos
Insua & French, 1991).
A lot of work on
MAUT
has dealt with incomplete information. (Sage & White, 1984)
proposed the model of imprecisely specified
ISMAUT
, where preference information about
both weights and utilities is assumed not to be precise. (Malakooti, 2000) suggested a new
efficient algorithm for ranking alternatives when there is incomplete information about the
preferences and the performance of the alternatives. This involves solving a single
mathematical programming problem many times. (Ahn, 2003) extended Malakooti's work.
(Eum et al., 2001) provided linear programming characterizations of dominance and
potential optimality for decision alternatives when information about performances and/or
weights is incomplete, extended the approach to hierarchical structures (Lee et al., 2002;
Park, 2004), and developed the concepts of
weak potential optimality
and
strong potential
optimality
(Park, 2004). More recently, (Mateos et al., 2007) considered the more general case
where imprecision, described by means of fixed bounds, appears in alternative
performances, as well as in weights and utilities.
The s
tochastic multicriteria acceptability analysis
(
SMAA
) and
SMAA-2
methods (Lahdelma &
Salminen, 1998; 2001) were developed for support in discrete group decision-making
problems, where weight information is absent. These methods explore the weight space in
order to describe the ratings that would make each alternative the preferred one. This
situation was also considered by other authors (Bana e Costa, 1986; Charnetski & Soland,
1978; Nijkamp et al., 1990; and Voogd, 1983).
(Sarabando & Dias, 2010) gives a brief overview of approaches proposed by different
authors within the
MAUT
and
MAVT
(multi-attribute value theory) framework to deal with
incomplete information.
2. The GMAA decision support system
The
generic multi-attribute analysis
(GMAA)
system
is a PC-based DSS based on an additive
multi-attribute utility model that is intended to allay many of the operational difficulties
involved in the DA cycle (Jiménez et al., 2003; 2006).
This cycle can be divided into four steps: 1) structuring the problem (which includes
specifying objectives, building a value hierarchy and establishing attributes for the lowest-
level objectives); 2) identifying the feasible alternatives, their performances and uncertainty
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