A NaP-preference (necessary and possible preference) is a pair of nested reflexive binary relations having a preorder as its smaller component, and satisfying natural forms of mixed completeness and mixed transitivity. A NaP-preference is normalized if its smaller component is a partial order. Dually, a strict NaP-preference is a pair of nested asymmetric binary relations having a strict partial order as its smaller component and satisfying suitable mixed transitivity properties.Weshow that normalized and strict NaPpreferences on the same ground set are in a one-to-one correspondence. It is known that a NaP-preference can be characterized by the existence of a set of total preorders whose intersection and union are respectively equal to its two components. In the same spirit, we characterize normalized and strict NaPpreferences by means of suitable families of order relations, respectively called injective and projective. The properties of injectivity and projectivity are a collectionwise extension of the antisymmetry and the completeness of a single binary relation.

Normalized and strict NaP-preferences

GIARLOTTA, Alfio
2015

Abstract

A NaP-preference (necessary and possible preference) is a pair of nested reflexive binary relations having a preorder as its smaller component, and satisfying natural forms of mixed completeness and mixed transitivity. A NaP-preference is normalized if its smaller component is a partial order. Dually, a strict NaP-preference is a pair of nested asymmetric binary relations having a strict partial order as its smaller component and satisfying suitable mixed transitivity properties.Weshow that normalized and strict NaPpreferences on the same ground set are in a one-to-one correspondence. It is known that a NaP-preference can be characterized by the existence of a set of total preorders whose intersection and union are respectively equal to its two components. In the same spirit, we characterize normalized and strict NaPpreferences by means of suitable families of order relations, respectively called injective and projective. The properties of injectivity and projectivity are a collectionwise extension of the antisymmetry and the completeness of a single binary relation.
Preference modeling; Antisymmetry; Completeness; NaP-preference; Injective family; Projective family
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/18368
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