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Resolving inconsistencies among constraints on the parameters of an MCDA model

Mousseau, Vincent; Dias, Luis; Figueira, José; Gomes da Silva, Carlos; Clìmaco, João (2003), Resolving inconsistencies among constraints on the parameters of an MCDA model, European Journal of Operational Research, 147, 1, p. 72-93. http://dx.doi.org/10.1016/S0377-2217(02)00233-3

Type
Article accepté pour publication ou publié
Date
2003
Journal name
European Journal of Operational Research
Volume
147
Number
1
Publisher
Elsevier
Pages
72-93
Publication identifier
http://dx.doi.org/10.1016/S0377-2217(02)00233-3
Metadata
Show full item record
Author(s)
Mousseau, Vincent
Dias, Luis
Figueira, José
Gomes da Silva, Carlos
Clìmaco, João
Abstract (EN)
We consider a framework where decision makers (DMs) interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the model’s parameters) and by analyzing the consequences of the information provided. DMs may introduce new constraints explicitly or implicitly (results that the model should yield). If a new constraint is incompatible with the previous ones, then the system becomes inconsistent and the DMs must choose between removing the new constraint or removing some of the older ones. We address the problem of identifying subsets of constraints which, when removed, lead to a consistent system. Identifying such subsets would indicate the reason for the inconsistent information given by DMs. There may exist several possibilities for the DMs to resolve the inconsistency. We present two algorithms to identify such possibilities, one using {0,1} mixed integer linear programming and the other one using linear programming. Both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint. The output of these algorithms helps the DM to identify the conflicting pieces of information in a set of statements he/she asserted. The relevance of these algorithms for MCDA is illustrated by an application to an aggregation/disaggregation procedure for the Electre Tri method.
Subjects / Keywords
Electre Tri; Multiple criteria analysis; Imprecise information; Aggregation/disaggregation approach; Inconsistent linear systems

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