A note on the asymmetric part of an outranking relation

Bouyssou, Denis; Pirlot, Marc

doi:10.1111/itor.12135

Cited by 4 publications

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“…The above analysis and review of prior research suggest that a combination of SMAA and outranking relation models can effectively solve stochastic MCDM problems with imprecise, partial, missing, or uncertain information. As one of the classical methods based on outranking relation models, the family of ELECTRE methods have been extensively studied and widely applied in various field (Buchanan and Vanderpooten, 2007;Covas et al, 2013;Wang et al, 2014a;Bouyssou and Pirlot, 2015;Govindan and Jepsen, 2016;Peng et al, 2016). ELECTRE III is the most popular method of this kind.…”

Section: Introductionmentioning

confidence: 99%

Stochastic multicriteria decision‐making approach based on SMAA‐ELECTRE with extended gray numbers

Zhou

Wang

Zhang

2017

Int Trans Operational Res

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Actual stochastic multicriteria decision‐making (MCDM) problems usually exhibit two forms of information loss: criteria value uncertainty and criteria weight uncertainty. In this paper, extended gray numbers (EGNs), integrated with discrete gray numbers and interval gray numbers are used to express the uncertainty of stochastic MCDM problems. Stochastic multicriteria acceptability analysis (SMAA) and ELECTRE III are combined to solve stochastic MCDM problems with uncertain weight information. First, the outranking relations on interval gray numbers and EGNs are defined. Then, a SMAA‐ELECTRE model for dealing with gray stochastic MCDM problems is constructed. Finally, an illustrative example and two comparative analyses are provided to verify the feasibility and usability of the proposed approach. The proposed approach provides recommendations for alternatives based on uncertain preference information. It therefore contributes a new way to solve stochastic MCDM problems with uncertain, imprecise, and/or missing preference information.

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Section: Introductionmentioning

confidence: 99%

Stochastic multicriteria decision‐making approach based on SMAA‐ELECTRE with extended gray numbers

Zhou

Wang

Zhang

2017

Int Trans Operational Res

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A consolidated approach to the axiomatization of outranking relations: a survey and new results

Bouyssou

Pirlot

2015

Ann Oper Res

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Outranking relations such as produced by the Electre I or II or the Tactic methods are based on a concordance and non-discordance principle that leads to declaring that an alternative is "superior" to another, if the coalition of attributes supporting this proposition is "sufficiently important" (concordance condition) and if there is no attribute that "strongly rejects" it (non-discordance condition). Such a way of comparing alternatives is rather natural and does not require a detailed analysis of tradeoffs between the various attributes. However, it is well known that it may produce binary relations that do not possess any remarkable property of transitivity or completeness. The axiomatic foundations of outranking relations have recently received attention. Within a conjoint measurement framework, characterizations of reflexive concordance-discordance relations have been obtained. These relations encompass those generated by the Electre I and II methods, which are non-strict (reflexive) relations. A different characterization has been provided for strict (asymmetric) preference relations such as produced by Tactic. In this paper we briefly review the various kinds of axiomatizations of outranking relations proposed so far in the literature. Then we analyze the relationships between reflexive and asymmetric outranking relations in a conjoint measurement framework, consolidating our previous work. Co-duality plays an essential rôle in our analysis. It allows us to understand the correspondence between the previous characterizations. Making a step further, we provide a common axiomatic characterization for both types of relations. Applying the co-duality operator to concordance-discordance relations also yields a new and interesting type of preference relation that we call concordance relation with bonus. The axiomatic characterization of such relations results directly from co-duality arguments.

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A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes

2022

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A note on the asymmetric part of an outranking relation

Cited by 4 publications

References 35 publications

Stochastic multicriteria decision‐making approach based on SMAA‐ELECTRE with extended gray numbers

Stochastic multicriteria decision‐making approach based on SMAA‐ELECTRE with extended gray numbers

A consolidated approach to the axiomatization of outranking relations: a survey and new results

A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes

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