(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.
C/O Luís Dias
Rua Antero de Quental, 199, 3000-033 Coimbra, PORTUGAL
Fax: +351 239 824692, e-mail: LDias@inescc.pt
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.
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