Secondary basis unique augmentation matroids and union minimal matroids
文献类型：期刊论文
| 作者 | Yao, Hua1; Zhu, William1; Wang, Fei-Yue2
|
| 刊名 | INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS
 |
| 出版日期 | 2014-12-01 |
| 卷号 | 5期号:6页码:955-962 |
| 关键词 | Granular computing Secondary basis unique augmentation matroid Rank-preserving weak-map Union minimal matroid Basis unique exchange matroid |
| 英文摘要 | By the augmentation axiom of matroids, given two independent sets whose cardinalities are not equal, there exists some other independent set of which the independent set with smaller cardinality is a proper subset. The augmentation axiom requires only the existence of independent set augmentation, not its uniqueness. This causes that the collections of bases of some matroids can be reduced while the unions of the collections of bases of these matroids remain unchanged. We may say these matroids are not minimal. This paper studies a type of matroids whose augmentations of independent sets have some degree of uniqueness and whose collections of bases are minimal in a sense. First, we propose the concept of secondary basis unique augmentation matroid, and prove a matroid is a secondary basis unique augmentation matroid iff the collection of the circuits of its dual matroid is a partition. Then we propose the concept of union minimal matroid based on rank-preserving weak-map, and prove that secondary basis unique augmentation matroids are union minimal matroids. Finally, we propose the concept of basis unique exchange matroid and study its properties. |
| WOS标题词 | Science & Technology ; Technology |
| 类目[WOS] | Computer Science, Artificial Intelligence |
| 研究领域[WOS] | Computer Science |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000348041000012 |
| 源URL | [http://ir.ia.ac.cn/handle/173211/3667]  |
| 专题 | 自动化研究所_复杂系统管理与控制国家重点实验室_先进控制与自动化团队 |
| 作者单位 | 1.Minnan Normal Univ, Lab Granular Comp, Zhangzhou 363000, Peoples R China 2.Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yao, Hua,Zhu, William,Wang, Fei-Yue. Secondary basis unique augmentation matroids and union minimal matroids[J]. INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS,2014,5(6):955-962. |
| APA | Yao, Hua,Zhu, William,&Wang, Fei-Yue.(2014).Secondary basis unique augmentation matroids and union minimal matroids.INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS,5(6),955-962. |
| MLA | Yao, Hua,et al."Secondary basis unique augmentation matroids and union minimal matroids".INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 5.6(2014):955-962. |
入库方式： OAI收割
来源：自动化研究所
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