Orders on Subsets Rationalised by Abstract Convex Geometries

Walter Bossert; Matthew J. Ryan; Arkadii Slinko

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Orders on Subsets Rationalised by Abstract Convex Geometries

机译：通过抽象凸几何合理化的子集顺序

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摘要

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.

机译：我们在有限集的子集上的阶上找到条件，这些条件对于任何两个子集按该次序的相对排名要由其相对于抽象凸几何的极端元素确定是必要和充分的。事实证明，这个问题与通过超级关系实现的与路径无关的选择功能的合理性密切相关。

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来源
《Order》 |2009年第3期|237-244|共8页
作者
Walter Bossert; Matthew J. Ryan; Arkadii Slinko;
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作者单位

CIREQ/Departement de sciences economiques. Universite de Montreal, Montreal, Canada;

Department of Economics, University of Auckland, Auckland, New Zealand;

Department of Mathematics, University of Auckland, Auckland, New Zealand;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
choice function; path independent; abstract convex geometry;

机译：选择功能与路径无关;抽象凸几何;

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1. Realization of abstract convex geometries by point configurations [J] . Adaricheva K, Wild M European journal of combinatorics . 2010,第1期

机译：通过点配置实现抽象凸几何
2. On the NBC-complexes and beta-invariants of abstract convex geometries [J] . Nakamura M Discrete Applied Mathematics . 2009,第8期

机译：关于抽象凸几何的NBC络合物和β不变量
3. The affine representation theorem for abstract convex geometries [J] . Kashiwabara K, Nakamura M, Okamoto Y Computational geometry: Theory and applications . 2005,第2期

机译：抽象凸几何的仿射表示定理
4. Rationalisation of Profiles of Abstract Argumentation Frameworks: Extended Abstract [C] . Stephane Airiau, Elise Bonzon, Ulle Endriss, International Joint Conference on Artificial Intelligence . 2019

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5. Geometry and Algorithms for Signal Recovery: From Convex Duality to Non-convex Formulations [D] . MacPhee, Kellie J. 2019

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6. Mechanical Adaptations of Epithelial Cells on Various Protruded Convex Geometries [O] . Sun-Min Yu, Bo Li, Steve Granick, 2020

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7. Realization of abstract convex geometries by point configurations [O] . Adaricheva Kira, Wild Marcel 2010

机译：通过点配置实现抽象凸几何
8. Extreme Points of Certain Convex Subsets of Log-Convex Functions [R] . Langberg, N. A., Leon, R. V., Lynch, J., 1979

机译：Log-Convex函数的某些凸子集的极值点

Orders on Subsets Rationalised by Abstract Convex Geometries

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