Consistent union and prioritized consistent union: new operations for preference aggregation

We discuss some new approaches to preference aggregation, keeping the natural property of transitivity of strict preferences in mind. In a previous paper, we discussed various ways in which to construct and process strict partial order relations in the context of ranking objects on the basis of mult...

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Vydáno v:Annals of operations research Ročník 195; číslo 1; s. 237 - 259
Hlavní autoři: Rademaker, Michaël, De Baets, Bernard
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.05.2012
Springer Science + Business Media
Springer
Springer Nature B.V
Témata:
Algorithms
Business and Management
Combinatorics
Decision making
Operations research
Operations Research/Decision Theory
Preferences
Process controls
Studies
Theory of Computation
Preference relation
Preference aggregation
Strict partial order relation
Transitivity
Decision support
ISSN:0254-5330, 1572-9338
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Shrnutí:We discuss some new approaches to preference aggregation, keeping the natural property of transitivity of strict preferences in mind. In a previous paper, we discussed various ways in which to construct and process strict partial order relations in the context of ranking objects on the basis of multiple criteria. We now broaden the scope to include more general expressions of preferences as inputs and introduce the concept of a NIP-triple, composed of a relation of necessary couples, a relation of impossible couples and a relation of possible couples. The use of NIP-triples allows for a more straightforward characterization of the consistent and prioritized consistent union as well as a smooth formulation of algorithmic implementations. We also introduce a NIP-triple closing operation, which can be combined with the consistent union operations for increased flexibility. Some properties of the proposed operations are examined. The consistent union operation is commutative, as is its composition with the closing operation. Both the consistent and prioritized consistent union are associative, but not when they are composed with the closing operation. Nevertheless, the composed operations surely have their use, which is also discussed.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-011-0852-0