Information interpretation of knowledge granularity
Information interpretation of knowledge granularity
复制标题
DOI：
10.3233/ifs-2012-0570
复制
发表时间：
2013-03
期刊：
影响因子：
--
通讯作者：
Ruizhi Wang;Duoqian Miao;Feifei Xu;Hongyun Zhang
中科院分区：
文献类型：
--
作者：
Ruizhi Wang;Duoqian Miao;Feifei Xu;Hongyun Zhang
知识粒度的定量分析对粒计算的发展提出了理论上的挑战。信息理论的措施已被提出来解决这个问题，表现出在完整的信息系统的有用性。然而，这些信息理论的措施和知识粒度之间的关系的数学分析还没有做。在本文中，引入Shannon的熵和互信息到完全信息系统，我们证明，为第一次，这些信息理论的措施单调减少分区变得粗糙下完全信息系统。此外，我们说明，他们的逆关系并不普遍成立，并提出了一个额外的条件下，逆关系是有效的。通过将Shannon熵推广到不完备信息系统，进一步讨论了基于覆盖广义粗糙集的广义Shannon熵即粗糙信息熵与知识粒度之间的关系。我们发现，在不完备信息系统中，粗糙信息熵随着覆盖的变粗而非单调变化。最后给出了一个实例来验证上述观测结果。
The quantitative analysis of the degree of knowledge granularity poses theoretical challenges for the development of granular computing. Information-theoretic measures have been proposed to address this problem, which exhibit usefulness in complete information systems. However, mathematical analysis of relationships between these information-theoretic measures and knowledge granularity has not been done. In this paper, after introducing Shannon's entropy and mutual information into complete information systems, we prove, for the first time, that these information-theoretic measures decrease monotonously as partition becomes coarser under complete information systems. Moreover, we illustrate that their inverse relationships do not hold generally and present an additional condition under which the inverse relationships are valid. By generalizing Shannon's entropy to incomplete information systems, we further discuss the relationship between the generalized Shannon's entropy termed as rough information entropy and knowledge granularity based on covering generalized rough sets. We find that in incomplete information systems, the rough information entropy varies nonmonotonously as covering becomes coarser. An illustrative example is given to verify the above observation result.