A Comparative Study of Algebra Viewpoint and Information Viewpoint in Attribute Reduction
A Comparative Study of Algebra Viewpoint and Information Viewpoint in Attribute Reduction
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发表时间：
2005-05
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通讯作者：
Guoyin Wang;Jun Zhao;J. An;Yuehua Wu
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作者：
Guoyin Wang;Jun Zhao;J. An;Yuehua Wu
属性约简是粗糙集理论中的一个重要问题，已经分别从粗糙集理论的代数观点和信息观点进行了研究。然而，基于这两种不同观点的属性约简概念并不等价。本文从这两个角度出发，对粗糙集理论的一些基本概念，如属性约简、属性重要性、核等之间的定量关系进行了比较研究。结果表明，这两个概念之间的关系与其说是等价的，不如说是包含的，这是因为从信息的角度讨论的粗糙集理论对属性和决策表的限制比从代数角度考虑时更具体。这两个观点的一致性将仅在一致的信息决策表中成立。也就是说，代数观点和信息观点对于一致的决策表是等价的，而对于不一致的决策表是不同的。研究结果对信息约简方法的设计和开发具有重要意义。
Attribute reduction is an important issue in rough set theory and has already been studied from the algebra viewpoint and information viewpoint of rough set theory respectively. However, the concepts of attribute reduction based on these two different viewpoints are not equivalent to each other. In this paper, we make a comparative study on the quantitative relationship between some basic concepts of rough set theory like attribute reduction, attribute significance and core defined from these two viewpoints. The results show that the relationship between these conceptions from the two viewpoints is rather an inclusion than an equivalence due to the fact that the rough set theory discussed from the information point of view restricts attributes and decision tables more specifically than it does when considered from the algebra point of view. The identity of the two viewpoints will hold in consistent information decision tables only. That is, the algebra viewpoint and information viewpoint are equivalent for a consistent decision table, while different for an inconsistent decision table. The results are significant for the design and development of methods for information reduction.