The graph-theoretical properties of partitions and information entropy

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	The graph-theoretical properties of partitions and information entropy
	Cao, CG ; Sui, YF ; Xia, YM
刊名	ROUGH SETS, FUZZY SETS, DATA MINING, AND GRANULAR COMPUTING, PRT 1, PROCEEDINGS
	2005
卷号	3641 页码:561-570
关键词	information systems information entropy classification partitions
ISSN号	0302-9743
英文摘要	The information entropy, as a measurement of the average amount of information contained in an information system, is used in the classification of objects and the analysis of information systems. The information entropy of a partition is non-increasing when the partition is refined, and is related to rough sets by Wong and Ziarko. The partitions and information entropy have some graph-theoretical properties. Given a non-empty universe U, all the partitions G on U are taken as nodes, and a relation V between partitions are defined and taken as edges. The graph obtained is denoted by (G, V), which represents the connections between partitions on U. According to the values of the information entropy of partitions, a directed graph (G, V) is defined on (C, V). It will be proved that there is a set of partitions with the minimal entropy; and a set of partitions with the maximal entropy; and the entropy is non-decreasing on any directed pathes in (G, V) from a partition with the minimal entropy to one of the partitions with the maximal entropy. Hence, in (G, V), the information entropy of partitions is represented in a clearly structured way.
WOS研究方向	Computer Science
语种	英语
出版者	SPRINGER-VERLAG BERLIN
WOS记录号	WOS:000232188600058
内容类型	期刊论文
源URL	[http://119.78.100.204/handle/2XEOYT63/10159]
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Cao, CG
作者单位	1.Chinese Acad Sci, Key Lab Intelligent Informat Proc, Inst Comp Technol, Beijing 100080, Peoples R China 2.Yunnan Normal Univ, Dept Comp Sci, Kunming 650092, Peoples R China
推荐引用方式 GB/T 7714	Cao, CG,Sui, YF,Xia, YM. The graph-theoretical properties of partitions and information entropy[J]. ROUGH SETS, FUZZY SETS, DATA MINING, AND GRANULAR COMPUTING, PRT 1, PROCEEDINGS,2005,3641:561-570.
APA	Cao, CG,Sui, YF,&Xia, YM.(2005).The graph-theoretical properties of partitions and information entropy.ROUGH SETS, FUZZY SETS, DATA MINING, AND GRANULAR COMPUTING, PRT 1, PROCEEDINGS,3641,561-570.
MLA	Cao, CG,et al."The graph-theoretical properties of partitions and information entropy".ROUGH SETS, FUZZY SETS, DATA MINING, AND GRANULAR COMPUTING, PRT 1, PROCEEDINGS 3641(2005):561-570.