Information Entropy and Granulation Co-Entropy of Partitions and Coverings: A Summary
Information Entropy and Granulation Co-Entropy of Partitions and Coverings: A Summary
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DOI：
10.1007/978-3-642-03281-3_2
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发表时间：
2009-07
期刊：
影响因子：
--
通讯作者：
D. Bianucci;G. Cattaneo
中科院分区：
文献类型：
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作者：
D. Bianucci;G. Cattaneo
将描述覆盖信息熵的一些方法以及覆盖的排序和准排序的一些定义，概括分区熵和排序的情况。目的是扩展到涵盖分区熵的反调性（严格递减单调性）的一般结果。特别讨论了不完整信息系统情况下的熵，并利用部分分区策略，将缺失的信息视为系统的特有值，并获得预期的反张力结果。另一方面，说明了一种从覆盖生成分区的方法。特别是，如果相对于覆盖上的某种准顺序关系，我们有一个覆盖γ比另一个覆盖δ更粗，则相对于分区上的标准偏序关系，诱导分区π(γ)结果比π(δ)更粗。因此，我们可以通过诱导分区的熵来比较两个覆盖。
Some approaches to the covering information entropy and some definitions of orderings and quasi–orderings of coverings will be described, generalizing the case of the partition entropy and ordering. The aim is to extend to covering the general result of anti–tonicity (strictly decreasing monotonicity) of partition entropy. In particular an entropy in the case of incomplete information systems is discussed, with the expected anti-tonicity result, making use of apartialpartition strategy in which the missing information is treated as a peculiar value of the system.On the other side, an approach to generate a partition from a covering is illustrated. In particular, if we have a coveringγcoarser than another coveringδwith respect to a certain quasi order relation on coverings, the induced partitionπ(γ) results to be coarser thanπ(δ) with respect to the standard partial ordering on partitions. Thus, one can compare the two coverings through the entropies of the induced partitions.