## Fuzzy outranking relations in ELECTRE providing manageable disaggregation procedures

### Authors: Vincent Mousseau and Luis Dias

ABSTRACT

{\indent In ELECTRE methods, the construction of an outranking relation $S$ amounts at validating or invalidating, for any pair of alternatives $(a,b) \in A$, an assertion $aSb$. This comparison is grounded on the evaluation vectors of both alternatives, and on additional information concerning the DM's preferences, accounting for two conditions: concordance and non-discordance.

In decision processes using these methods, the analyst should interact with DM(s) in order to elicit values for preferential parameters. This can be done either directly or through a disaggregation procedure that infers the parameters values from holistic judgements provided by the DM(s). Inference is usually performed through an optimization program that accounts for the aggregation model and minimizes an error function". Although disaggregation approaches have been largely used in additive models, only few advances have been made towards a disaggregation approach for ELECTRE methods. This probably reflects the optimization unfriendly" character of the most recent ELECTRE methods.

In this paper we are concerned with a slight adaptation of the fuzzy outranking relation used in the ELECTRE III and ELECTRE TRI that preserves the original ideas and is more optimization-friendly for parameter inference programs. Such modification is shown to preserve the original discordance concept. We show that the modified outranking relation makes it easier to solve inference programs.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-27.ps.gz