This paper proposes a general definition of an undominated maximal of a relation on a constraint set. No specific requirement is imposed on either the asymmetry of the objective relation or the constraint set (which might, or might not, coincide with the ground set of the objective relation). Several characterizations are formulated that express undominated maximals of an objective relation as maximals of some trace associated with that objective relation. By means of some of these characterizations, the structure of the entire set of undominated maximals is examined in the particular case of relations induced by open and closed convex cones—among them, the weak and strong Pareto dominance—and, in the case of semiorders, that admit certain types of representability. The results of the last part of the examination allow the construction of many examples of relations whose entire sets of maximals and undominated maximals are completely identifiable in an elementary way.
Undominated maximals: general definition and characterizations / Federico Quartieri. - In: MATHEMATICS. - ISSN 2227-7390. - ELETTRONICO. - 11:(2023), pp. 3879.0-3879.0. [10.3390/math11183879]
Undominated maximals: general definition and characterizations
Federico Quartieri
2023
Abstract
This paper proposes a general definition of an undominated maximal of a relation on a constraint set. No specific requirement is imposed on either the asymmetry of the objective relation or the constraint set (which might, or might not, coincide with the ground set of the objective relation). Several characterizations are formulated that express undominated maximals of an objective relation as maximals of some trace associated with that objective relation. By means of some of these characterizations, the structure of the entire set of undominated maximals is examined in the particular case of relations induced by open and closed convex cones—among them, the weak and strong Pareto dominance—and, in the case of semiorders, that admit certain types of representability. The results of the last part of the examination allow the construction of many examples of relations whose entire sets of maximals and undominated maximals are completely identifiable in an elementary way.File | Dimensione | Formato | |
---|---|---|---|
Mathematics 2023 - mathematics-11-03879-v2.pdf
accesso aperto
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Open Access
Dimensione
368.78 kB
Formato
Adobe PDF
|
368.78 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.