(1) INESC Coimbra, Rua Antero de Quental, 199, 3000-033 Coimbra,
Portugal
(2) Faculdade de Economia, Universidade de Coimbra, Av. Dias da Silva
165, 3004-512 Coimbra, Portugal
(3) LAMSADE, Université Paris-Dauphine, Place du Maréchal
De Lattre de Tassigny, 75775 Paris Cedex 16, France
(4) Escola Superior de Tecnologia e Gestão, Instituto Politécnico
de Leiria, 2401-951 Leiria, Portugal
IRIS (Interactive Robustness analysis and parameters' Inference
for multicriteria Sorting) is a Decision Support Software designed to address
the problem of sorting a set of actions (alternatives, projects, candidates,
etc.) into predefined ordered categories, according to their evaluations
(performances) on multiple criteria. For instance, it may be used to sort
funding requests according to merit categories (e.g. “Very good”, “Good”,
“Fair”, “Not eligible”), or to sort loan applicants into categories (e.g.
“Accept”, “Require more collateral”, “Reject”), or to sort employees in
a company into categories that define incentive packages, etc.
IRIS implements the methodology presented in Dias et al. (2002), using
a pessimistic concordance-only variant of the ELECTRE TRI method. Rather
than demanding precise values for the ELECTRE TRI parameters, IRIS allows
to enter constraints on these values, namely assignment examples that it
tries to restore. It adds a module to identify the source of inconsistency
among the constraints when it is not possible to respect all of them at
the same time, according to a method described in Mousseau et al. (2002).
On the other hand, if the constraints are compatible with multiple assignments
for the actions, IRIS allows drawing robust conclusions by indicating the
range of assignments (for each action) that do not contradict any constraint.
The main characteristics of IRIS are the following:
Figure 1. The proposed sorting does not restore the assignment example
that a1 belongs to C3 due to inconsistent constraints. It corresponds to
the parameter values indicated on the right bottom of the screen.
Figure 2. Given an inconsistent system of constraints (on the left),
IRIS suggests five alternative ways to restore the consistency by removing
constraints. The first suggestion is to remove constraint no. 2; the fifth
suggestion is to remove constraints no. 7, 8, and 12.
Figure 3. There is a range of categories where each action may be assigned
to without violating any constraint (e.g. a robust conclusion is that a2
is not worse than C3). The proposed assignment (darker cell) corresponds
to the inferred parameter values shown in the last row of the grid on the
right. The parameter values shown in the penultimate line of that grid
lead to the assignment of a28 to C5, corresponding to the selected cell.
If the user chooses another cell these values will change. IRIS also shows
that a28 cannot be assigned to C2, regardless of the parameter values that
are chosen.
Figure 4. (Left:) the constraints define a 7-dimension polytope of
very small volume; from the combinations of parameter values that satisfy
the bounds, about 14.3% also respect the remaining constraints. (Right:)
the geometric mean of the number of categories where each action may be
assigned (respecting all the constraints) is now 1.357, which is less 47.7%
relatively to the previous iteration.
MORE INFORMATION
INESC Coimbra
C/O Luís Dias
Rua Antero de Quental, 199, 3000-033 Coimbra, PORTUGAL
Fax: +351 239 824692, e-mail: LDias@inescc.pt
http://www4.fe.uc.pt/lmcdias/iris.htm
REFERENCES
Mousseau, V. J. Figueira, L. Dias, C. Gomes da Silva, J. Clímaco
(2002), "Resolving inconsistencies among constraints on the parameters
of an MCDA model", to appear in the European Journal of Operational Research.
Dias, L., V. Mousseau, J. Figueira, J. Clímaco (2002), "An Aggregation/Disaggregation
Approach to Obtain Robust Conclusions with ELECTRE TRI", European Journal
of Operational Research, vol 138, 332-348.