Orders on Subsets Rationalised by Abstract Convex Geometries
نویسندگان
چکیده
منابع مشابه
Orders on Subsets Rationalised by Abstract Convex Geometries
We find conditions on the order on subsets of a finite set which are necessary and sufficient for the relative ranking of any two subsets in this order to be determined by their extreme elements relative to an abstract convex geometry. It turns out that this question is closely related to the rationalisability of path independent choice functions by hyper-relations.
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The following classical example of convex geometries shows how they earned their name. Given a set of points X in Euclidean space R, one defines a closure operator on X as follows: for any Y ⊆ X, Y = convex hull(Y ) ∩ X. One easily verifies that such an operator satisfies the anti-exchange axiom. Thus, (X,−) is a convex geometry. Denote by Co(R, X) the closure lattice of this closure space, nam...
متن کاملChoice functions and abstract convex geometries *
A main aim of this paper is to make connections between two well – but up to now independently – developed theories, the theory of choice functions and the theory of closure operators. It is shown that the classes of ordinally rationalizable and path independent choice functions are related to the classes of distributive and anti-exchange closures. 1999 Elsevier Science B.V. All rights reserved.
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We consider a system of linear inequalities and its associated polyhedron for which we can maximize any linear objective function by /nding tight inequalities at an optimal solution in a greedy way. We call such a system of inequalities a dual greedy system and its associated polyhedron a dual greedy polyhedron. Such dual greedy systems have been considered by Faigle and Kern, and Kr1 uger for ...
متن کاملThe affine representation theorem for abstract convex geometries
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ژورنال
عنوان ژورنال: Order
سال: 2009
ISSN: 0167-8094,1572-9273
DOI: 10.1007/s11083-009-9121-0