Methodology by:
IRIS software design and
development by: Luis Dias(1,2),
Vincent Mousseau(3), Carlos Gomes Silva(1,4)
(1) INESC Coimbra, Rua Antero de
Quental, 199, 3000-033 Coimbra, PORTUGAL
(2) Faculdade de
Economia da 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 problems) is a
Decision Support Software designed to address the problem of sorting a set of
actions (alternatives, projects, candidates) into predefined ordered categories,
according to their evaluations (performances) at 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 reconstitute. 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. (2003). 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 or IRIS (version 2.0) are:
· IRIS implements a variant of the pessimistic ELECTRE TRI, where the outranking relation is defined as proposed by Mousseau and Dias (2002).
·
IRIS
accepts imprecision concerning the criteria weights and the cutting level, which
are treated as variables (whereas category profiles, indifference, preference
and veto thresholds are fixed by the user). The
users may indicate intervals for each of these parameters, as well as linear
constraints, rather than being forced to indicate precise values
for all these parameters. Furthermore, the constraints may be defined indirectly,
as indicated in the next item.
·
IRIS
accepts assignment examples, where the users indicate minimum and maximum
categories for some of the actions, according to their holistic judgment (e.g.
“action a1 is a typical
element of C3”, or
“action a2 should be
placed in category C3 or
higher”, or “I hesitate: action a2
should be placed in category C3
or C4”). These assignment
examples are translated into constraints on the parameter values, meaning that
the assignments of ELECTRE TRI should restore these examples.
·
When the
constraints are inconsistent, IRIS infers a combination of parameter values that
least violates the constraints, by minimizing the maximum deviation. Then, it
shows the sorting that corresponds to these parameter values (see example in
Fig. 1). Furthermore, a module
becomes available to determine the alternative subsets of constraints that must
be removed to restore the consistency (see example in Fig. 2).
·
When the
constraints are consistent, IRIS infers a "central" combination of
parameter values by minimizing the maximum slack. For each action, it depicts
the category corresponding to that combination, as well as the range of
categories where the action might be assigned without violating any constraint (robustness
analysis). For each category in the range IRIS may also determine a combination
of parameter values that assigns the action to that category (see example in
Fig. 3).
·
Moreover,
when the constraints are consistent, IRIS may compute some indicators concerning
the precision of the inputs (by estimating the volume of the polyhedron of all
feasible combinations of parameter values) and the precision of the outputs (by
indicating the geometric mean of the number of possible assignments per action).
See example in Fig. 4.
These
features allow decision makers to build sorting models in a progressive and
interactive manner, where the output at a given iteration is used to guide the
revision of the input for the following iteration. The general idea is to start
with few constraints of the parameter values, adding more inequalities as a
product of an interactive learning process about the problem and the method.
This process should aim at progressively reducing the set of accepted
combinations of parameter values, until the end users (decision makers, problem
owners) are satisfied with the results’ precision, and yet comfortable with
and confident about the constraints introduced.
The
final outputs of the procedure are:
·
a set of
constraints and assignment examples defining a set of acceptable combinations of
parameter values;
·
an
inferred combination of parameter values defining a model in a precise manner;
·
a precise
assignment or range of assignments for each action in A
that is robust with respect to the constraints inserted.
However, the most important outcome may be
that the end users will increase the insight on their view of the problem, learn
about their preferences, and will possibly modify their opinions.
 |
Figure 1. The proposed sorting does not reconstitute the assignment example that a1 belongs to C3 due to inconsistent constraints. The proposed sorting 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 respect 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. |
Download Demo Version (limited problem sizes): IrisDemo.zip (570 KB)
MORE INFORMATION AND SALES
C/O Prof. Luis Dias
Rua Antero de Quental, 199, 3000-033 Coimbra, PORTUGAL
Fax: +351 239 824692, e-mail: LDias@inescc.pt
This page: http://www4.fe.uc.pt/lmcdias/iris.htm
DOCUMENTATION
Dias, L., V. Mousseau, IRIS - Interactive Robustness analysis and parameters' Inference for multicriteria Sorting problems (Version 2.0) - User Manual, Documents of INESC Coimbra, No. 1/2003. IrisMan2.pdf (357 KB)
REFERENCES
Dias, L.C., V. Mousseau (2003), “IRIS: A DSS for Multiple Criteria Sorting Problems”, Journal of Multi-Criteria Decision Analysis, Vol. 12, 285-298.
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.
Dias, L., V. Mousseau, IRIS: um SAD para problemas de classificação baseado em agregação multicritério, Actas da 3ª Conferência da Associação Portuguesa de Sistemas de Informação (3ª CAPSI), Coimbra, 20-22 Novembro de 2002. (in Portuguese) [DiasMous2.pdf (100 KB)]
Mousseau V., L. Dias (2004), "Valued outranking relations in Electre providing manageable disaggregation procedures", European Journal of Operational Research, Vol. 156, No. 2, 467-482.
Mousseau, V., J. Figueira, L. Dias, C. Gomes da Silva, J. Clímaco, "Resolving inconsistencies among constraints on the parameters of an MCDA model", European Journal of Operational Research, Vol. 147, No. 1, 72-93, 2003.
Luis M. C. Dias - Software page / Luis M. C. Dias - Página de Software
